Comparison between EM and gradient ascent for tracking a simulated mouse

The code below compares the expectation maximization (EM) and gradient ascent algorithm for tracking a simulated mouse.

import numpy as np
import torch
import plotly.graph_objs as go

import lds.tracking.utils
import lds.simulation
import lds.learning

Simulation

We will simulate a linear dynamical system for tracking. The parameters of this model are highlighted in red.

\[\begin{split}\begin{equation} \begin{alignedat}{4} & x_n&&=A x_{n-1}+w_n&&\quad with\quad&&w_n\sim\mathcal{N}(0,\textcolor{red}{\sigma_a^2}Q_e),&&\quad x_n\in\mathbb{R}^6&&\label{eq:lds}\\ & y_n&&=C x_n+v_n&&\quad with\quad&&v_n\sim\mathcal{N}(0,R),&&\quad y_n\in\mathbb{R}^2,&&\quad R=\left[\begin{array}{c,c} \textcolor{red}{\sigma_x^2}&0\\ 0&\textcolor{red}{\sigma_y^2} \end{array}\right]\\ & x_0&&\in\mathcal{N}(\textcolor{red}{m_0},\textcolor{red}{V_0})&& && \end{alignedat} \end{equation}\end{split}\]

Define simulation parameters

pos_x0 = 0.0
pos_y0 = 0.0
vel_x0 = 0.0
vel_y0 = 0.0
acc_x0 = 0.0
acc_y0 = 0.0
dt = 1e-1
num_pos = 500
sigma_a_true = 0.1
sigma_x = 5e-0
sigma_y = 5e-0
sqrt_diag_V0_value = 1e-3

B, _, Z, R, Qe = lds.tracking.utils.getLDSmatricesForTracking(
    dt=dt, sigma_a=np.nan, sigma_x=sigma_x, sigma_y=sigma_y)
Q_true = Qe*sigma_a_true**2
sqrt_diag_R = np.array([sigma_x, sigma_y])
m0 = np.array([pos_x0, vel_x0, acc_x0, pos_y0, vel_y0, acc_y0],
              dtype=np.double)
sqrt_diag_V0 = np.ones(6)*sqrt_diag_V0_value
V0 = np.diag(sqrt_diag_V0**2)

Perform simulation

Code for lds.simulation.simulateLDS

x0, x, y = lds.simulation.simulateLDS(N=num_pos, B=B, Q=Q_true, Z=Z, R=R,
                                             m0=m0, V0=V0)

Plot simulated state and measurement positions

fig = go.Figure()
trace_x = go.Scatter(x=x[0, :], y=x[3, :], mode="lines+markers",
                     showlegend=True, name="pos. state mean")
trace_y = go.Scatter(x=y[0, :], y=y[1, :], mode="lines+markers",
                     showlegend=True, name="measurement", opacity=0.3)
trace_start = go.Scatter(x=[x0[0]], y=[x0[3]], mode="markers",
                         text="initial state", marker={"size": 7},
                         showlegend=False)
fig.add_trace(trace_x)
fig.add_trace(trace_y)
fig.add_trace(trace_start)
fig.update_layout(xaxis_title="horizontal direction",
                  yaxis_title="vertical direction")
fig

Estimation of the \(\sigma_a^2\) parameter only

sigma_a0 = 0.25
ga_vars_to_estimate = {"sigma_a": True, "sqrt_diag_R": False,
                       "m0": False, "sqrt_diag_V0": False}
em_vars_to_estimate = {"sigma_a": True, "R": False,
                       "m0": False, "V0": False}
em_max_iter = 200
lbfgs_max_iter = 2
lbfgs_n_epochs = 100
lbfgs_tolerance_grad = 1e-9
lbfgs_tolerance_change = 1e-7

Grid search

sigma_a_min = 0.001
sigma_a_max = 2.0
sigma_a_step = 0.005
sqrt_noise_intensities = np.arange(sigma_a_min, sigma_a_max, sigma_a_step)
gs_log_likes = np.empty(len(sqrt_noise_intensities))
for i, sigma_a in enumerate(sqrt_noise_intensities):
    Q_gs = Qe * sigma_a**2
    filterRes = lds.inference.filterLDS_SS_withMissingValues_np(
        y=y, B=B, Q=Q_gs, m0=m0, V0=V0, Z=Z, R=R)
    gs_log_likes[i] = filterRes["logLike"]
    print(f"log likelihood for sigma_a={sigma_a:.04f}: {gs_log_likes[i]}")
argmax = np.argmax(gs_log_likes)
gs_max_ll = gs_log_likes[argmax]
gs_max_sigma_a = sqrt_noise_intensities[argmax]
print(f"max log likelihood: {gs_max_ll}, "
      f"max sigma_a: {gs_max_sigma_a}")

/home/runner/work/lds_python/lds_python/examples/sphinx_gallery/tracking/plotEMvsGAcomparisonSimulated.py:119: DeprecationWarning:

Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)

log likelihood for sigma_a=0.0010: -43918.15047716407
log likelihood for sigma_a=0.0060: -5130.17821834068
log likelihood for sigma_a=0.0110: -3772.9272671372546
log likelihood for sigma_a=0.0160: -3426.4577715444875
log likelihood for sigma_a=0.0210: -3284.0039942527337
log likelihood for sigma_a=0.0260: -3210.9373614341484
log likelihood for sigma_a=0.0310: -3168.388567568668
log likelihood for sigma_a=0.0360: -3141.4804037333806
log likelihood for sigma_a=0.0410: -3123.4451259452694
log likelihood for sigma_a=0.0460: -3110.8244869368236
log likelihood for sigma_a=0.0510: -3101.6968271681417
log likelihood for sigma_a=0.0560: -3094.923905750769
log likelihood for sigma_a=0.0610: -3089.7963947051194
log likelihood for sigma_a=0.0660: -3085.853435447271
log likelihood for sigma_a=0.0710: -3082.7849255563415
log likelihood for sigma_a=0.0760: -3080.375862058028
log likelihood for sigma_a=0.0810: -3078.4732686193756
log likelihood for sigma_a=0.0860: -3076.965817628233
log likelihood for sigma_a=0.0910: -3075.770871968114
log likelihood for sigma_a=0.0960: -3074.8260124302783
log likelihood for sigma_a=0.1010: -3074.083358846615
log likelihood for sigma_a=0.1060: -3073.5056779295373
log likelihood for sigma_a=0.1110: -3073.06366136901
log likelihood for sigma_a=0.1160: -3072.7339871826903
log likelihood for sigma_a=0.1210: -3072.497915743548
log likelihood for sigma_a=0.1260: -3072.3402574564097
log likelihood for sigma_a=0.1310: -3072.248603093169
log likelihood for sigma_a=0.1360: -3072.2127426219486
log likelihood for sigma_a=0.1410: -3072.224221231915
log likelihood for sigma_a=0.1460: -3072.275996526377
log likelihood for sigma_a=0.1510: -3072.36217122379
log likelihood for sigma_a=0.1560: -3072.477782846374
log likelihood for sigma_a=0.1610: -3072.618636865967
log likelihood for sigma_a=0.1660: -3072.7811733081103
log likelihood for sigma_a=0.1710: -3072.96235934583
log likelihood for sigma_a=0.1760: -3073.1596022493854
log likelihood for sigma_a=0.1810: -3073.370678402362
log likelihood for sigma_a=0.1860: -3073.5936750897
log likelihood for sigma_a=0.1910: -3073.826942506446
log likelihood for sigma_a=0.1960: -3074.0690539975867
log likelihood for sigma_a=0.2010: -3074.318772964821
log likelihood for sigma_a=0.2060: -3074.5750252033904
log likelihood for sigma_a=0.2110: -3074.8368756843824
log likelihood for sigma_a=0.2160: -3075.1035089939724
log likelihood for sigma_a=0.2210: -3075.3742127948735
log likelihood for sigma_a=0.2260: -3075.648363796003
log likelihood for sigma_a=0.2310: -3075.9254158123867
log likelihood for sigma_a=0.2360: -3076.204889573647
log likelihood for sigma_a=0.2410: -3076.4863640001754
log likelihood for sigma_a=0.2460: -3076.769468716539
log likelihood for sigma_a=0.2510: -3077.0538776098933
log likelihood for sigma_a=0.2560: -3077.3393032745944
log likelihood for sigma_a=0.2610: -3077.625492210252
log likelihood for sigma_a=0.2660: -3077.912220662569
log likelihood for sigma_a=0.2710: -3078.1992910130584
log likelihood for sigma_a=0.2760: -3078.486528639909
log likelihood for sigma_a=0.2810: -3078.773779182565
log likelihood for sigma_a=0.2860: -3079.060906155383
log likelihood for sigma_a=0.2910: -3079.3477888609254
log likelihood for sigma_a=0.2960: -3079.6343205635003
log likelihood for sigma_a=0.3010: -3079.9204068874596
log likelihood for sigma_a=0.3060: -3080.2059644108363
log likelihood for sigma_a=0.3110: -3080.4909194292145
log likelihood for sigma_a=0.3160: -3080.7752068667387
log likelihood for sigma_a=0.3210: -3081.058769316734
log likelihood for sigma_a=0.3260: -3081.3415561948814
log likelihood for sigma_a=0.3310: -3081.623522990957
log likelihood for sigma_a=0.3360: -3081.9046306068185
log likelihood for sigma_a=0.3410: -3082.1848447705856
log likelihood for sigma_a=0.3460: -3082.4641355172294
log likelihood for sigma_a=0.3510: -3082.7424767273897
log likelihood for sigma_a=0.3560: -3083.0198457184188
log likelihood for sigma_a=0.3610: -3083.296222880431
log likelihood for sigma_a=0.3660: -3083.5715913526365
log likelihood for sigma_a=0.3710: -3083.845936735097
log likelihood for sigma_a=0.3760: -3084.1192468318486
log likelihood for sigma_a=0.3810: -3084.3915114218457
log likelihood for sigma_a=0.3860: -3084.662722054269
log likelihood for sigma_a=0.3910: -3084.932871866228
log likelihood for sigma_a=0.3960: -3085.2019554188073
log likelihood for sigma_a=0.4010: -3085.4699685514456
log likelihood for sigma_a=0.4060: -3085.7369082508762
log likelihood for sigma_a=0.4110: -3086.0027725338427
log likelihood for sigma_a=0.4160: -3086.267560342022
log likelihood for sigma_a=0.4210: -3086.531271447891
log likelihood for sigma_a=0.4260: -3086.7939063696112
log likelihood for sigma_a=0.4310: -3087.0554662954246
log likelihood for sigma_a=0.4360: -3087.315953014853
log likelihood for sigma_a=0.4410: -3087.5753688575332
log likelihood for sigma_a=0.4460: -3087.8337166374445
log likelihood for sigma_a=0.4510: -3088.0909996032615
log likelihood for sigma_a=0.4560: -3088.3472213930286
log likelihood for sigma_a=0.4610: -3088.6023859941956
log likelihood for sigma_a=0.4660: -3088.8564977063725
log likelihood for sigma_a=0.4710: -3089.1095611085307
log likelihood for sigma_a=0.4760: -3089.3615810291153
log likelihood for sigma_a=0.4810: -3089.6125625189075
log likelihood for sigma_a=0.4860: -3089.862510826745
log likelihood for sigma_a=0.4910: -3090.111431377285
log likelihood for sigma_a=0.4960: -3090.359329750696
log likelihood for sigma_a=0.5010: -3090.606211665153
log likelihood for sigma_a=0.5060: -3090.8520829594586
log likelihood for sigma_a=0.5110: -3091.096949578819
log likelihood for sigma_a=0.5160: -3091.340817560943
log likelihood for sigma_a=0.5210: -3091.5836930236055
log likelihood for sigma_a=0.5260: -3091.825582153702
log likelihood for sigma_a=0.5310: -3092.0664911968383
log likelihood for sigma_a=0.5360: -3092.3064264479135
log likelihood for sigma_a=0.5410: -3092.5453942431823
log likelihood for sigma_a=0.5460: -3092.7834009519534
log likelihood for sigma_a=0.5510: -3093.0204529698576
log likelihood for sigma_a=0.5560: -3093.2565567124634
log likelihood for sigma_a=0.5610: -3093.491718609456
log likelihood for sigma_a=0.5660: -3093.7259450990914
log likelihood for sigma_a=0.5710: -3093.9592426235163
log likelihood for sigma_a=0.5760: -3094.1916176245286
log likelihood for sigma_a=0.5810: -3094.4230765389666
log likelihood for sigma_a=0.5860: -3094.6536257954617
log likelihood for sigma_a=0.5910: -3094.883271810995
log likelihood for sigma_a=0.5960: -3095.1120209875744
log likelihood for sigma_a=0.6010: -3095.339879709618
log likelihood for sigma_a=0.6060: -3095.5668543414668
log likelihood for sigma_a=0.6110: -3095.7929512245073
log likelihood for sigma_a=0.6160: -3096.0181766757664
log likelihood for sigma_a=0.6210: -3096.2425369853113
log likelihood for sigma_a=0.6260: -3096.4660384147287
log likelihood for sigma_a=0.6310: -3096.6886871954985
log likelihood for sigma_a=0.6360: -3096.9104895273267
log likelihood for sigma_a=0.6410: -3097.1314515770728
log likelihood for sigma_a=0.6460: -3097.3515794771647
log likelihood for sigma_a=0.6510: -3097.5708793246463
log likelihood for sigma_a=0.6560: -3097.7893571803456
log likelihood for sigma_a=0.6610: -3098.0070190674614
log likelihood for sigma_a=0.6660: -3098.2238709712797
log likelihood for sigma_a=0.6710: -3098.4399188378693
log likelihood for sigma_a=0.6760: -3098.6551685738204
log likelihood for sigma_a=0.6810: -3098.869626045518
log likelihood for sigma_a=0.6860: -3099.083297078442
log likelihood for sigma_a=0.6910: -3099.296187456935
log likelihood for sigma_a=0.6960: -3099.5083029234625
log likelihood for sigma_a=0.7010: -3099.7196491785935
log likelihood for sigma_a=0.7060: -3099.9302318803434
log likelihood for sigma_a=0.7110: -3100.1400566440952
log likelihood for sigma_a=0.7160: -3100.349129042298
log likelihood for sigma_a=0.7210: -3100.557454604101
log likelihood for sigma_a=0.7260: -3100.7650388154652
log likelihood for sigma_a=0.7310: -3100.9718871190175
log likelihood for sigma_a=0.7360: -3101.1780049135473
log likelihood for sigma_a=0.7410: -3101.3833975544485
log likelihood for sigma_a=0.7460: -3101.5880703533944
log likelihood for sigma_a=0.7510: -3101.7920285782325
log likelihood for sigma_a=0.7560: -3101.9952774532967
log likelihood for sigma_a=0.7610: -3102.197822159134
log likelihood for sigma_a=0.7660: -3102.3996678327644
log likelihood for sigma_a=0.7710: -3102.6008195675827
log likelihood for sigma_a=0.7760: -3102.801282413555
log likelihood for sigma_a=0.7810: -3103.001061377357
log likelihood for sigma_a=0.7860: -3103.200161422418
log likelihood for sigma_a=0.7910: -3103.398587468843
log likelihood for sigma_a=0.7960: -3103.5963443941105
log likelihood for sigma_a=0.8010: -3103.793437032808
log likelihood for sigma_a=0.8060: -3103.989870176809
log likelihood for sigma_a=0.8110: -3104.1856485756043
log likelihood for sigma_a=0.8160: -3104.3807769364003
log likelihood for sigma_a=0.8210: -3104.5752599246503
log likelihood for sigma_a=0.8260: -3104.769102163674
log likelihood for sigma_a=0.8310: -3104.9623082354283
log likelihood for sigma_a=0.8360: -3105.1548826803805
log likelihood for sigma_a=0.8410: -3105.3468299979354
log likelihood for sigma_a=0.8460: -3105.538154646819
log likelihood for sigma_a=0.8510: -3105.7288610449086
log likelihood for sigma_a=0.8560: -3105.9189535698
log likelihood for sigma_a=0.8610: -3106.108436559244
log likelihood for sigma_a=0.8660: -3106.2973143107683
log likelihood for sigma_a=0.8710: -3106.4855910829356
log likelihood for sigma_a=0.8760: -3106.6732710946158
log likelihood for sigma_a=0.8810: -3106.8603585257824
log likelihood for sigma_a=0.8860: -3107.046857518082
log likelihood for sigma_a=0.8910: -3107.2327721744878
log likelihood for sigma_a=0.8960: -3107.418106559917
log likelihood for sigma_a=0.9010: -3107.602864701554
log likelihood for sigma_a=0.9060: -3107.787050589286
log likelihood for sigma_a=0.9110: -3107.9706681754537
log likelihood for sigma_a=0.9160: -3108.1537213759775
log likelihood for sigma_a=0.9210: -3108.3362140699483
log likelihood for sigma_a=0.9260: -3108.518150100104
log likelihood for sigma_a=0.9310: -3108.6995332736205
log likelihood for sigma_a=0.9360: -3108.880367361778
log likelihood for sigma_a=0.9410: -3109.0606561005925
log likelihood for sigma_a=0.9460: -3109.240403190988
log likelihood for sigma_a=0.9510: -3109.419612299347
log likelihood for sigma_a=0.9560: -3109.598287057715
log likelihood for sigma_a=0.9610: -3109.7764310638827
log likelihood for sigma_a=0.9660: -3109.954047881922
log likelihood for sigma_a=0.9710: -3110.1311410427143
log likelihood for sigma_a=0.9760: -3110.3077140437567
log likelihood for sigma_a=0.9810: -3110.483770349689
log likelihood for sigma_a=0.9860: -3110.659313392834
log likelihood for sigma_a=0.9910: -3110.8343465733274
log likelihood for sigma_a=0.9960: -3111.0088732593417
log likelihood for sigma_a=1.0010: -3111.1828967874285
log likelihood for sigma_a=1.0060: -3111.3564204628865
log likelihood for sigma_a=1.0110: -3111.529447560144
log likelihood for sigma_a=1.0160: -3111.7019813229554
log likelihood for sigma_a=1.0210: -3111.874024964667
log likelihood for sigma_a=1.0260: -3112.045581668655
log likelihood for sigma_a=1.0310: -3112.2166545885543
log likelihood for sigma_a=1.0360: -3112.387246848272
log likelihood for sigma_a=1.0410: -3112.557361543068
log likelihood for sigma_a=1.0460: -3112.7270017389
log likelihood for sigma_a=1.0510: -3112.8961704734584
log likelihood for sigma_a=1.0560: -3113.0648707560217
log likelihood for sigma_a=1.0610: -3113.233105567841
log likelihood for sigma_a=1.0660: -3113.400877862655
log likelihood for sigma_a=1.0710: -3113.5681905667893
log likelihood for sigma_a=1.0760: -3113.7350465793425
log likelihood for sigma_a=1.0810: -3113.9014487724457
log likelihood for sigma_a=1.0860: -3114.0673999920905
log likelihood for sigma_a=1.0910: -3114.2329030577457
log likelihood for sigma_a=1.0960: -3114.397960762694
log likelihood for sigma_a=1.1010: -3114.5625758749534
log likelihood for sigma_a=1.1060: -3114.7267511367077
log likelihood for sigma_a=1.1110: -3114.890489265136
log likelihood for sigma_a=1.1160: -3115.0537929525135
log likelihood for sigma_a=1.1210: -3115.21666486635
log likelihood for sigma_a=1.1260: -3115.3791076498196
log likelihood for sigma_a=1.1310: -3115.541123922111
log likelihood for sigma_a=1.1360: -3115.7027162783434
log likelihood for sigma_a=1.1410: -3115.8638872901365
log likelihood for sigma_a=1.1460: -3116.0246395057857
log likelihood for sigma_a=1.1510: -3116.1849754503587
log likelihood for sigma_a=1.1560: -3116.344897626228
log likelihood for sigma_a=1.1610: -3116.504408512997
log likelihood for sigma_a=1.1660: -3116.6635105679693
log likelihood for sigma_a=1.1710: -3116.8222062264713
log likelihood for sigma_a=1.1760: -3116.980497901687
log likelihood for sigma_a=1.1810: -3117.1383879853133
log likelihood for sigma_a=1.1860: -3117.295878847669
log likelihood for sigma_a=1.1910: -3117.4529728377292
log likelihood for sigma_a=1.1960: -3117.6096722836455
log likelihood for sigma_a=1.2010: -3117.765979492966
log likelihood for sigma_a=1.2060: -3117.921896752389
log likelihood for sigma_a=1.2110: -3118.0774263285994
log likelihood for sigma_a=1.2160: -3118.232570468279
log likelihood for sigma_a=1.2210: -3118.3873313982085
log likelihood for sigma_a=1.2260: -3118.5417113253184
log likelihood for sigma_a=1.2310: -3118.69571243754
log likelihood for sigma_a=1.2360: -3118.8493369032894
log likelihood for sigma_a=1.2410: -3119.002586872267
log likelihood for sigma_a=1.2460: -3119.1554644750076
log likelihood for sigma_a=1.2510: -3119.307971824016
log likelihood for sigma_a=1.2560: -3119.46011101283
log likelihood for sigma_a=1.2610: -3119.6118841173447
log likelihood for sigma_a=1.2660: -3119.76329319505
log likelihood for sigma_a=1.2710: -3119.9143402861037
log likelihood for sigma_a=1.2760: -3120.0650274125865
log likelihood for sigma_a=1.2810: -3120.2153565795743
log likelihood for sigma_a=1.2860: -3120.365329774845
log likelihood for sigma_a=1.2910: -3120.5149489689375
log likelihood for sigma_a=1.2960: -3120.6642161160007
log likelihood for sigma_a=1.3010: -3120.813133152981
log likelihood for sigma_a=1.3060: -3120.961702000943
log likelihood for sigma_a=1.3110: -3121.1099245641526
log likelihood for sigma_a=1.3160: -3121.257802731022
log likelihood for sigma_a=1.3210: -3121.40533837401
log likelihood for sigma_a=1.3260: -3121.5525333498094
log likelihood for sigma_a=1.3310: -3121.699389499408
log likelihood for sigma_a=1.3360: -3121.8459086485736
log likelihood for sigma_a=1.3410: -3121.9920926075633
log likelihood for sigma_a=1.3460: -3122.137943171676
log likelihood for sigma_a=1.3510: -3122.283462121336
log likelihood for sigma_a=1.3560: -3122.428651222
log likelihood for sigma_a=1.3610: -3122.5735122246706
log likelihood for sigma_a=1.3660: -3122.718046865989
log likelihood for sigma_a=1.3710: -3122.862256867927
log likelihood for sigma_a=1.3760: -3123.0061439386177
log likelihood for sigma_a=1.3810: -3123.1497097722645
log likelihood for sigma_a=1.3860: -3123.292956048803
log likelihood for sigma_a=1.3910: -3123.435884434866
log likelihood for sigma_a=1.3960: -3123.5784965834505
log likelihood for sigma_a=1.4010: -3123.720794134066
log likelihood for sigma_a=1.4060: -3123.862778712879
log likelihood for sigma_a=1.4110: -3124.004451932992
log likelihood for sigma_a=1.4160: -3124.1458153947224
log likelihood for sigma_a=1.4210: -3124.2868706853087
log likelihood for sigma_a=1.4260: -3124.427619379338
log likelihood for sigma_a=1.4310: -3124.568063038614
log likelihood for sigma_a=1.4360: -3124.708203212951
log likelihood for sigma_a=1.4410: -3124.848041439525
log likelihood for sigma_a=1.4460: -3124.987579243265
log likelihood for sigma_a=1.4510: -3125.12681813711
log likelihood for sigma_a=1.4560: -3125.2657596222657
log likelihood for sigma_a=1.4610: -3125.4044051880096
log likelihood for sigma_a=1.4660: -3125.5427563116396
log likelihood for sigma_a=1.4710: -3125.680814459388
log likelihood for sigma_a=1.4760: -3125.81858108557
log likelihood for sigma_a=1.4810: -3125.956057633641
log likelihood for sigma_a=1.4860: -3126.0932455354196
log likelihood for sigma_a=1.4910: -3126.2301462118658
log likelihood for sigma_a=1.4960: -3126.366761072938
log likelihood for sigma_a=1.5010: -3126.5030915176417
log likelihood for sigma_a=1.5060: -3126.6391389343694
log likelihood for sigma_a=1.5110: -3126.7749047007546
log likelihood for sigma_a=1.5160: -3126.910390184027
log likelihood for sigma_a=1.5210: -3127.0455967407306
log likelihood for sigma_a=1.5260: -3127.180525717296
log likelihood for sigma_a=1.5310: -3127.315178450047
log likelihood for sigma_a=1.5360: -3127.4495562649145
log likelihood for sigma_a=1.5410: -3127.583660478012
log likelihood for sigma_a=1.5460: -3127.7174923954226
log likelihood for sigma_a=1.5510: -3127.8510533135623
log likelihood for sigma_a=1.5560: -3127.98434451914
log likelihood for sigma_a=1.5610: -3128.1173672890955
log likelihood for sigma_a=1.5660: -3128.2501228909246
log likelihood for sigma_a=1.5710: -3128.3826125828055
log likelihood for sigma_a=1.5760: -3128.514837613467
log likelihood for sigma_a=1.5810: -3128.6467992224384
log likelihood for sigma_a=1.5860: -3128.778498640216
log likelihood for sigma_a=1.5910: -3128.9099370880526
log likelihood for sigma_a=1.5960: -3129.04111577851
log likelihood for sigma_a=1.6010: -3129.172035915077
log likelihood for sigma_a=1.6060: -3129.302698692443
log likelihood for sigma_a=1.6110: -3129.433105296794
log likelihood for sigma_a=1.6160: -3129.563256905514
log likelihood for sigma_a=1.6210: -3129.693154687538
log likelihood for sigma_a=1.6260: -3129.8227998033226
log likelihood for sigma_a=1.6310: -3129.9521934052254
log likelihood for sigma_a=1.6360: -3130.081336636842
log likelihood for sigma_a=1.6410: -3130.210230634096
log likelihood for sigma_a=1.6460: -3130.338876524394
log likelihood for sigma_a=1.6510: -3130.467275427198
log likelihood for sigma_a=1.6560: -3130.595428454302
log likelihood for sigma_a=1.6610: -3130.723336709142
log likelihood for sigma_a=1.6660: -3130.8510012878787
log likelihood for sigma_a=1.6710: -3130.9784232784104
log likelihood for sigma_a=1.6760: -3131.1056037612716
log likelihood for sigma_a=1.6810: -3131.2325438095377
log likelihood for sigma_a=1.6860: -3131.359244488474
log likelihood for sigma_a=1.6910: -3131.4857068560445
log likelihood for sigma_a=1.6960: -3131.6119319629697
log likelihood for sigma_a=1.7010: -3131.7379208523716
log likelihood for sigma_a=1.7060: -3131.8636745605295
log likelihood for sigma_a=1.7110: -3131.989194116195
log likelihood for sigma_a=1.7160: -3132.114480541212
log likelihood for sigma_a=1.7210: -3132.2395348504124
log likelihood for sigma_a=1.7260: -3132.3643580516373
log likelihood for sigma_a=1.7310: -3132.488951145762
log likelihood for sigma_a=1.7360: -3132.6133151270233
log likelihood for sigma_a=1.7410: -3132.7374509827823
log likelihood for sigma_a=1.7460: -3132.8613596935024
log likelihood for sigma_a=1.7510: -3132.9850422333034
log likelihood for sigma_a=1.7560: -3133.1084995695364
log likelihood for sigma_a=1.7610: -3133.2317326632738
log likelihood for sigma_a=1.7660: -3133.354742468799
log likelihood for sigma_a=1.7710: -3133.4775299341422
log likelihood for sigma_a=1.7760: -3133.6000960012357
log likelihood for sigma_a=1.7810: -3133.7224416052927
log likelihood for sigma_a=1.7860: -3133.844567675533
log likelihood for sigma_a=1.7910: -3133.966475135101
log likelihood for sigma_a=1.7960: -3134.0881649008966
log likelihood for sigma_a=1.8010: -3134.20963788359
log likelihood for sigma_a=1.8060: -3134.3308949884
log likelihood for sigma_a=1.8110: -3134.4519371139068
log likelihood for sigma_a=1.8160: -3134.572765153434
log likelihood for sigma_a=1.8210: -3134.6933799939147
log likelihood for sigma_a=1.8260: -3134.8137825168833
log likelihood for sigma_a=1.8310: -3134.933973597969
log likelihood for sigma_a=1.8360: -3135.05395410713
log likelihood for sigma_a=1.8410: -3135.1737249087982
log likelihood for sigma_a=1.8460: -3135.293286861611
log likelihood for sigma_a=1.8510: -3135.4126408188927
log likelihood for sigma_a=1.8560: -3135.5317876283484
log likelihood for sigma_a=1.8610: -3135.650728132169
log likelihood for sigma_a=1.8660: -3135.769463167552
log likelihood for sigma_a=1.8710: -3135.887993565808
log likelihood for sigma_a=1.8760: -3136.0063201533635
log likelihood for sigma_a=1.8810: -3136.1244437511173
log likelihood for sigma_a=1.8860: -3136.2423651750023
log likelihood for sigma_a=1.8910: -3136.3600852357167
log likelihood for sigma_a=1.8960: -3136.477604738731
log likelihood for sigma_a=1.9010: -3136.5949244845324
log likelihood for sigma_a=1.9060: -3136.712045268778
log likelihood for sigma_a=1.9110: -3136.8289678816677
log likelihood for sigma_a=1.9160: -3136.945693108879
log likelihood for sigma_a=1.9210: -3137.0622217312102
log likelihood for sigma_a=1.9260: -3137.178554524214
log likelihood for sigma_a=1.9310: -3137.2946922590904
log likelihood for sigma_a=1.9360: -3137.410635701818
log likelihood for sigma_a=1.9410: -3137.526385614175
log likelihood for sigma_a=1.9460: -3137.641942752711
log likelihood for sigma_a=1.9510: -3137.7573078697837
log likelihood for sigma_a=1.9560: -3137.8724817126977
log likelihood for sigma_a=1.9610: -3137.9874650246447
log likelihood for sigma_a=1.9660: -3138.1022585439982
log likelihood for sigma_a=1.9710: -3138.2168630046053
log likelihood for sigma_a=1.9760: -3138.3312791360026
log likelihood for sigma_a=1.9810: -3138.4455076632603
log likelihood for sigma_a=1.9860: -3138.5595493070286
log likelihood for sigma_a=1.9910: -3138.6734047836803
log likelihood for sigma_a=1.9960: -3138.787074805171
max log likelihood: -3072.2127426219486, max sigma_a: 0.136

Gradient acent

Code for lds.learning.torch_lbfgs_optimize_SS_tracking_diagV0

sqrt_diag_R_torch = torch.DoubleTensor([sigma_x, sigma_y])
m0_torch = torch.from_numpy(m0)
sqrt_diag_V0_torch = torch.DoubleTensor([sqrt_diag_V0_value
                                         for i in range(len(m0))])
y_torch = torch.from_numpy(y.astype(np.double))
B_torch = torch.from_numpy(B.astype(np.double))
Qe_torch = torch.from_numpy(Qe.astype(np.double))
Z_torch = torch.from_numpy(Z.astype(np.double))
optim_res_ga = lds.learning.torch_lbfgs_optimize_SS_tracking_diagV0(
    y=y_torch, B=B_torch, sigma_a0=sigma_a0,
    Qe=Qe_torch, Z=Z_torch, sqrt_diag_R_0=sqrt_diag_R_torch, m0_0=m0_torch,
    sqrt_diag_V0_0=sqrt_diag_V0_torch, max_iter=lbfgs_max_iter,
    n_epochs=lbfgs_n_epochs,
    vars_to_estimate=ga_vars_to_estimate, tolerance_grad=lbfgs_tolerance_grad,
    tolerance_change=lbfgs_tolerance_change)

/home/runner/work/lds_python/lds_python/src/lds/inference.py:390: UserWarning:

The use of `x.T` on tensors of dimension other than 2 to reverse their shape is deprecated and it will throw an error in a future release. Consider `x.mT` to transpose batches of matrices or `x.permute(*torch.arange(x.ndim - 1, -1, -1))` to reverse the dimensions of a tensor. (Triggered internally at ../aten/src/ATen/native/TensorShape.cpp:3697.)

in closure, ll=-3076.9969058091638
in closure, ll=-3101.751293847748
in closure, ll=-3263.7595600488194
in closure, ll=-3073.469848487592
in closure, ll=-3072.286009995906
--------------------------------------------------------------------------------
epoch: 0
likelihood: -3076.9969058091638
sigma_a:
tensor([0.1467], dtype=torch.float64, requires_grad=True)
in closure, ll=-3072.286009995906
in closure, ll=-3073.139602581781
in closure, ll=-3072.2118596883347
--------------------------------------------------------------------------------
epoch: 1
likelihood: -3072.286009995906
sigma_a:
tensor([0.1365], dtype=torch.float64, requires_grad=True)
in closure, ll=-3072.2118596883347
in closure, ll=-3072.211476296811
--------------------------------------------------------------------------------
epoch: 2
likelihood: -3072.2118596883347
sigma_a:
tensor([0.1373], dtype=torch.float64, requires_grad=True)
in closure, ll=-3072.211476296811
in closure, ll=-3072.211466384449
--------------------------------------------------------------------------------
epoch: 3
likelihood: -3072.211476296811
sigma_a:
tensor([0.1372], dtype=torch.float64, requires_grad=True)
in closure, ll=-3072.211466384449
--------------------------------------------------------------------------------
epoch: 4
likelihood: -3072.211466384449
sigma_a:
tensor([0.1372], dtype=torch.float64, requires_grad=True)
in closure, ll=-3072.211466384449
--------------------------------------------------------------------------------
epoch: 5
likelihood: -3072.211466384449
sigma_a:
tensor([0.1372], dtype=torch.float64, requires_grad=True)

EM

Code for lds.learning.em_SS_tracking

Qe_reg_param = 1e-5
Qe_regularized = Qe + Qe_reg_param*np.eye(Qe.shape[0])
optim_res_em = lds.learning.em_SS_tracking(
    y=y, B=B, sigma_a0=sigma_a0,
    Qe=Qe_regularized, Z=Z, R_0=R, m0_0=m0, V0_0=V0,
    vars_to_estimate=em_vars_to_estimate, max_iter=em_max_iter)

LogLike[0000]=-3076.997001
sigma_a=0.250000
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0001]=-3076.961984
sigma_a=0.249385
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0002]=-3076.927712
sigma_a=0.248783
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0003]=-3076.894094
sigma_a=0.248192
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0004]=-3076.860954
sigma_a=0.247609
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0005]=-3076.827140
sigma_a=0.247014
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0006]=-3076.794366
sigma_a=0.246437
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0007]=-3076.761275
sigma_a=0.245854
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0008]=-3076.729015
sigma_a=0.245285
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0009]=-3076.696243
sigma_a=0.244708
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0010]=-3076.664979
sigma_a=0.244156
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0011]=-3076.632482
sigma_a=0.243582
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0012]=-3076.601894
sigma_a=0.243042
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0013]=-3076.570641
sigma_a=0.242490
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0014]=-3076.538847
sigma_a=0.241927
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0015]=-3076.507301
sigma_a=0.241369
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0016]=-3076.476077
sigma_a=0.240816
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0017]=-3076.445371
sigma_a=0.240272
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0018]=-3076.414871
sigma_a=0.239731
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0019]=-3076.384211
sigma_a=0.239187
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0020]=-3076.355105
sigma_a=0.238671
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0021]=-3076.324659
sigma_a=0.238130
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0022]=-3076.294496
sigma_a=0.237594
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0023]=-3076.265795
sigma_a=0.237083
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0024]=-3076.235995
sigma_a=0.236553
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0025]=-3076.205950
sigma_a=0.236017
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0026]=-3076.177869
sigma_a=0.235517
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0027]=-3076.149277
sigma_a=0.235007
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0028]=-3076.120473
sigma_a=0.234492
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0029]=-3076.091342
sigma_a=0.233972
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0030]=-3076.062386
sigma_a=0.233454
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0031]=-3076.033532
sigma_a=0.232937
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0032]=-3076.005529
sigma_a=0.232436
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0033]=-3075.978037
sigma_a=0.231943
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0034]=-3075.950093
sigma_a=0.231442
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0035]=-3075.920503
sigma_a=0.230910
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0036]=-3075.893115
sigma_a=0.230418
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0037]=-3075.865836
sigma_a=0.229927
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0038]=-3075.839121
sigma_a=0.229446
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0039]=-3075.812516
sigma_a=0.228967
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0040]=-3075.784842
sigma_a=0.228468
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0041]=-3075.758838
sigma_a=0.227998
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0042]=-3075.733771
sigma_a=0.227545
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0043]=-3075.707813
sigma_a=0.227076
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0044]=-3075.681253
sigma_a=0.226595
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0045]=-3075.654834
sigma_a=0.226116
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0046]=-3075.628170
sigma_a=0.225632
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0047]=-3075.604036
sigma_a=0.225194
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0048]=-3075.579034
sigma_a=0.224739
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0049]=-3075.553228
sigma_a=0.224270
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0050]=-3075.527788
sigma_a=0.223807
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0051]=-3075.503190
sigma_a=0.223358
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0052]=-3075.478105
sigma_a=0.222900
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0053]=-3075.453424
sigma_a=0.222449
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0054]=-3075.428845
sigma_a=0.222000
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0055]=-3075.404828
sigma_a=0.221560
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0056]=-3075.380846
sigma_a=0.221120
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0057]=-3075.356539
sigma_a=0.220674
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0058]=-3075.333953
sigma_a=0.220259
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0059]=-3075.310446
sigma_a=0.219827
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0060]=-3075.286339
sigma_a=0.219383
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0061]=-3075.262999
sigma_a=0.218953
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0062]=-3075.239846
sigma_a=0.218525
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0063]=-3075.216176
sigma_a=0.218088
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0064]=-3075.192806
sigma_a=0.217656
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0065]=-3075.169622
sigma_a=0.217226
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0066]=-3075.147334
sigma_a=0.216813
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0067]=-3075.125194
sigma_a=0.216402
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0068]=-3075.102284
sigma_a=0.215976
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0069]=-3075.079213
sigma_a=0.215546
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0070]=-3075.057515
sigma_a=0.215142
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0071]=-3075.034315
sigma_a=0.214709
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0072]=-3075.011696
sigma_a=0.214286
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0073]=-3074.989413
sigma_a=0.213869
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0074]=-3074.967475
sigma_a=0.213458
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0075]=-3074.946480
sigma_a=0.213064
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0076]=-3074.925019
sigma_a=0.212661
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0077]=-3074.903228
sigma_a=0.212251
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0078]=-3074.883210
sigma_a=0.211874
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0079]=-3074.862476
sigma_a=0.211482
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0080]=-3074.841813
sigma_a=0.211092
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0081]=-3074.822255
sigma_a=0.210722
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0082]=-3074.801062
sigma_a=0.210320
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0083]=-3074.780024
sigma_a=0.209921
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0084]=-3074.760054
sigma_a=0.209542
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0085]=-3074.739943
sigma_a=0.209159
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0086]=-3074.719850
sigma_a=0.208776
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0087]=-3074.699835
sigma_a=0.208394
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0088]=-3074.679987
sigma_a=0.208015
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0089]=-3074.660892
sigma_a=0.207649
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0090]=-3074.641365
sigma_a=0.207275
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0091]=-3074.622744
sigma_a=0.206917
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0092]=-3074.603010
sigma_a=0.206538
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0093]=-3074.583240
sigma_a=0.206157
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0094]=-3074.564031
sigma_a=0.205787
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0095]=-3074.545415
sigma_a=0.205427
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0096]=-3074.527095
sigma_a=0.205072
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0097]=-3074.510594
sigma_a=0.204752
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0098]=-3074.492773
sigma_a=0.204406
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0099]=-3074.475099
sigma_a=0.204063
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0100]=-3074.456710
sigma_a=0.203705
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0101]=-3074.439077
sigma_a=0.203361
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0102]=-3074.420902
sigma_a=0.203006
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0103]=-3074.404066
sigma_a=0.202676
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0104]=-3074.386718
sigma_a=0.202336
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0105]=-3074.368604
sigma_a=0.201980
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0106]=-3074.350079
sigma_a=0.201616
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0107]=-3074.331939
sigma_a=0.201259
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0108]=-3074.313731
sigma_a=0.200899
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0109]=-3074.295810
sigma_a=0.200545
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0110]=-3074.277426
sigma_a=0.200180
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0111]=-3074.261263
sigma_a=0.199859
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0112]=-3074.242526
sigma_a=0.199487
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0113]=-3074.226199
sigma_a=0.199161
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0114]=-3074.209141
sigma_a=0.198821
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0115]=-3074.193479
sigma_a=0.198508
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0116]=-3074.176050
sigma_a=0.198158
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0117]=-3074.158534
sigma_a=0.197807
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0118]=-3074.142443
sigma_a=0.197483
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0119]=-3074.126811
sigma_a=0.197168
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0120]=-3074.110998
sigma_a=0.196849
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0121]=-3074.095516
sigma_a=0.196535
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0122]=-3074.078270
sigma_a=0.196186
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0123]=-3074.061940
sigma_a=0.195854
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0124]=-3074.045679
sigma_a=0.195523
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0125]=-3074.030350
sigma_a=0.195211
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0126]=-3074.014912
sigma_a=0.194895
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0127]=-3073.999325
sigma_a=0.194576
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0128]=-3073.985043
sigma_a=0.194283
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0129]=-3073.971028
sigma_a=0.193995
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0130]=-3073.955647
sigma_a=0.193678
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0131]=-3073.940515
sigma_a=0.193365
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0132]=-3073.926477
sigma_a=0.193075
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0133]=-3073.911913
sigma_a=0.192773
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0134]=-3073.896915
sigma_a=0.192462
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0135]=-3073.883508
sigma_a=0.192182
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0136]=-3073.869866
sigma_a=0.191898
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0137]=-3073.857138
sigma_a=0.191632
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0138]=-3073.842944
sigma_a=0.191335
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0139]=-3073.829004
sigma_a=0.191042
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0140]=-3073.815793
sigma_a=0.190764
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0141]=-3073.803052
sigma_a=0.190496
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0142]=-3073.789278
sigma_a=0.190205
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0143]=-3073.775556
sigma_a=0.189914
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0144]=-3073.762021
sigma_a=0.189627
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0145]=-3073.749194
sigma_a=0.189355
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0146]=-3073.735767
sigma_a=0.189069
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0147]=-3073.722514
sigma_a=0.188786
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0148]=-3073.709438
sigma_a=0.188506
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0149]=-3073.695373
sigma_a=0.188204
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0150]=-3073.682524
sigma_a=0.187928
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0151]=-3073.670337
sigma_a=0.187665
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0152]=-3073.657709
sigma_a=0.187392
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0153]=-3073.646087
sigma_a=0.187140
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0154]=-3073.633986
sigma_a=0.186878
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0155]=-3073.622048
sigma_a=0.186618
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0156]=-3073.609324
sigma_a=0.186341
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0157]=-3073.597067
sigma_a=0.186073
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0158]=-3073.586034
sigma_a=0.185831
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0159]=-3073.573400
sigma_a=0.185554
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0160]=-3073.561142
sigma_a=0.185284
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0161]=-3073.550040
sigma_a=0.185039
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0162]=-3073.540024
sigma_a=0.184818
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0163]=-3073.528194
sigma_a=0.184556
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0164]=-3073.515679
sigma_a=0.184278
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0165]=-3073.504294
sigma_a=0.184024
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0166]=-3073.493446
sigma_a=0.183782
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0167]=-3073.482875
sigma_a=0.183545
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0168]=-3073.470220
sigma_a=0.183262
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0169]=-3073.458556
sigma_a=0.182999
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0170]=-3073.446731
sigma_a=0.182732
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0171]=-3073.434989
sigma_a=0.182467
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0172]=-3073.424452
sigma_a=0.182228
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0173]=-3073.413739
sigma_a=0.181984
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0174]=-3073.403982
sigma_a=0.181762
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0175]=-3073.394292
sigma_a=0.181541
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0176]=-3073.383693
sigma_a=0.181298
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0177]=-3073.373979
sigma_a=0.181075
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0178]=-3073.363611
sigma_a=0.180836
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0179]=-3073.353551
sigma_a=0.180604
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0180]=-3073.343215
sigma_a=0.180365
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0181]=-3073.332591
sigma_a=0.180118
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0182]=-3073.322708
sigma_a=0.179888
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0183]=-3073.312270
sigma_a=0.179645
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0184]=-3073.302845
sigma_a=0.179425
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0185]=-3073.293584
sigma_a=0.179207
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0186]=-3073.283356
sigma_a=0.178967
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0187]=-3073.273509
sigma_a=0.178735
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0188]=-3073.263533
sigma_a=0.178499
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0189]=-3073.253256
sigma_a=0.178255
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0190]=-3073.243461
sigma_a=0.178022
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0191]=-3073.233977
sigma_a=0.177796
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0192]=-3073.226351
sigma_a=0.177614
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0193]=-3073.217113
sigma_a=0.177392
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0194]=-3073.208361
sigma_a=0.177182
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0195]=-3073.198410
sigma_a=0.176942
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0196]=-3073.190073
sigma_a=0.176740
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0197]=-3073.181049
sigma_a=0.176521
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0198]=-3073.172323
sigma_a=0.176309
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]
LogLike[0199]=-3073.163954
sigma_a=0.176105
R:
[[25.  0.]
 [ 0. 25.]]
m0:
[0. 0. 0. 0. 0. 0.]
V0:
[[1.e-06 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 1.e-06 0.e+00 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 1.e-06 0.e+00 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 1.e-06 0.e+00 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 1.e-06 0.e+00]
 [0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 1.e-06]]

Plots

Convergence

fig = go.Figure()
trace = go.Scatter(x=optim_res_ga["elapsed_time"], y=optim_res_ga["log_like"],
                  name="Gradient ascent", mode="lines+markers")
fig.add_trace(trace)
trace = go.Scatter(x=optim_res_em["elapsed_time"], y=optim_res_em["log_like"],
                   name="EM", mode="lines+markers")
fig.add_trace(trace)
fig.update_layout(xaxis_title="Elapsed Time (sec)",
                  yaxis_title="Log Likelihood")
fig

\(\sigma_a\) estimates

fig = go.Figure()
trace = go.Bar(x=["Grid Search", "Gradient Ascent", "EM"],
               y=[gs_max_sigma_a**2,
                  optim_res_ga["estimates"]["sigma_a"].item()**2,
                  optim_res_em["estimates"]["sigma_a"]**2])
fig.add_trace(trace)
fig.add_hline(y=sigma_a_true**2)
fig.update_layout(xaxis_title="Estimation Method",
                  yaxis_title=r"$\sigma_a$")
fig

Estimation of all parameters

pos_x0_0 = 0.1
pos_y0_0 = -0.1
vel_x0_0 = 0.01
vel_y0_0 = -0.01
acc_x0_0 = 0.001
acc_y0_0 = -0.001
sqrt_diag_V0_value0 = 1e-2
sigma_a0 = 0.25
sigma_x_0 = 5e-2
sigma_y_0 = 5e-2
ga_vars_to_estimate = {"sigma_a": True, "sqrt_diag_R": True, "m0": True,
                       "sqrt_diag_V0": True}
em_vars_to_estimate = {"sigma_a": True, "R": True, "m0": True,
                       "V0": True}
em_max_iter = 400
lbfgs_max_iter = 2
lbfgs_n_epochs = 200
lbfgs_tolerance_grad = 1e-9
lbfgs_tolerance_change = 1e-7

m0_0 = np.array([pos_x0_0, vel_x0_0, acc_x0_0, pos_y0_0, vel_y0_0, acc_y0_0])
sqrt_diag_V0_0 = np.array([sqrt_diag_V0_value0 for i in range(len(m0_0))])
sqrt_diag_R_0 = np.array([sigma_x_0, sigma_y_0])

Gradient acent

Code for lds.learning.torch_lbfgs_optimize_SS_tracking_diagV0

m0_0_torch = torch.from_numpy(m0_0)
sqrt_diag_V0_0_torch = torch.from_numpy(sqrt_diag_V0_0)
sqrt_diag_R_0_torch = torch.from_numpy(sqrt_diag_R_0)

y_torch = torch.from_numpy(y.astype(np.double))
B_torch = torch.from_numpy(B.astype(np.double))
Qe_torch = torch.from_numpy(Qe.astype(np.double))
Z_torch = torch.from_numpy(Z.astype(np.double))
optim_res_ga = lds.learning.torch_lbfgs_optimize_SS_tracking_diagV0(
    y=y_torch, B=B_torch, sigma_a0=sigma_a0,
    Qe=Qe_torch, Z=Z_torch, sqrt_diag_R_0=sqrt_diag_R_0_torch, m0_0=m0_0_torch,
    sqrt_diag_V0_0=sqrt_diag_V0_0_torch, max_iter=lbfgs_max_iter,
    n_epochs=lbfgs_n_epochs,
    vars_to_estimate=ga_vars_to_estimate, tolerance_grad=lbfgs_tolerance_grad,
    tolerance_change=lbfgs_tolerance_change)

in closure, ll=-4232161.786494465
in closure, ll=-38392.29151902456
--------------------------------------------------------------------------------
epoch: 0
likelihood: -4232161.786494465
sigma_a:
tensor([0.2544], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([0.5589, 0.5363], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 0.1000,  0.0100,  0.0010, -0.1000, -0.0100, -0.0010],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([0.0102, 0.0100, 0.0100, 0.0101, 0.0100, 0.0100], dtype=torch.float64,
       requires_grad=True)
in closure, ll=-38392.29151902456
in closure, ll=-38336.84494797784
in closure, ll=-38088.602095022696
in closure, ll=-36766.193372262
in closure, ll=-30626.089427820472
--------------------------------------------------------------------------------
epoch: 1
likelihood: -38392.29151902456
sigma_a:
tensor([0.2568], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([0.6236, 0.6077], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 0.1001,  0.0100,  0.0010, -0.1000, -0.0100, -0.0010],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([0.0102, 0.0100, 0.0100, 0.0101, 0.0100, 0.0100], dtype=torch.float64,
       requires_grad=True)
in closure, ll=-30626.089427820472
in closure, ll=-19756.337153924676
--------------------------------------------------------------------------------
epoch: 2
likelihood: -30626.089427820472
sigma_a:
tensor([0.2636], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([0.7887, 0.7645], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 0.1003,  0.0101,  0.0010, -0.1001, -0.0101, -0.0010],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([0.0103, 0.0100, 0.0100, 0.0102, 0.0100, 0.0100], dtype=torch.float64,
       requires_grad=True)
in closure, ll=-19756.337153924676
in closure, ll=-14102.316343412878
--------------------------------------------------------------------------------
epoch: 3
likelihood: -19756.337153924676
sigma_a:
tensor([0.2714], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([0.9481, 0.9210], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 0.1006,  0.0103,  0.0010, -0.1003, -0.0103, -0.0011],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([0.0103, 0.0100, 0.0100, 0.0102, 0.0100, 0.0100], dtype=torch.float64,
       requires_grad=True)
in closure, ll=-14102.316343412878
in closure, ll=-9974.936705147738
--------------------------------------------------------------------------------
epoch: 4
likelihood: -14102.316343412878
sigma_a:
tensor([0.2831], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([1.1598, 1.1259], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 0.1011,  0.0105,  0.0011, -0.1006, -0.0106, -0.0011],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([0.0103, 0.0100, 0.0100, 0.0102, 0.0100, 0.0100], dtype=torch.float64,
       requires_grad=True)
in closure, ll=-9974.936705147738
in closure, ll=-7365.940151154489
--------------------------------------------------------------------------------
epoch: 5
likelihood: -9974.936705147738
sigma_a:
tensor([0.2975], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([1.4056, 1.3650], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 0.1018,  0.0109,  0.0011, -0.1011, -0.0110, -0.0012],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([0.0103, 0.0100, 0.0100, 0.0102, 0.0100, 0.0100], dtype=torch.float64,
       requires_grad=True)
in closure, ll=-7365.940151154489
in closure, ll=-5648.951040661185
--------------------------------------------------------------------------------
epoch: 6
likelihood: -7365.940151154489
sigma_a:
tensor([0.3136], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([1.7032, 1.6539], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 0.1030,  0.0114,  0.0011, -0.1019, -0.0117, -0.0012],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([0.0102, 0.0100, 0.0100, 0.0102, 0.0100, 0.0100], dtype=torch.float64,
       requires_grad=True)
in closure, ll=-5648.951040661185
in closure, ll=-4560.848874005544
--------------------------------------------------------------------------------
epoch: 7
likelihood: -5648.951040661185
sigma_a:
tensor([0.3266], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([2.0527, 1.9936], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 0.1048,  0.0122,  0.0012, -0.1032, -0.0127, -0.0013],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([0.0101, 0.0099, 0.0100, 0.0101, 0.0100, 0.0100], dtype=torch.float64,
       requires_grad=True)
in closure, ll=-4560.848874005544
in closure, ll=-3883.736729060867
--------------------------------------------------------------------------------
epoch: 8
likelihood: -4560.848874005544
sigma_a:
tensor([0.3262], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([2.4591, 2.3890], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 0.1074,  0.0133,  0.0012, -0.1051, -0.0143, -0.0012],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([0.0099, 0.0098, 0.0100, 0.0101, 0.0099, 0.0100], dtype=torch.float64,
       requires_grad=True)
in closure, ll=-3883.736729060867
in closure, ll=-3479.138234167048
--------------------------------------------------------------------------------
epoch: 9
likelihood: -3883.736729060867
sigma_a:
tensor([0.2916], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([2.9189, 2.8369], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 0.1114,  0.0150,  0.0012, -0.1079, -0.0165, -0.0009],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([0.0097, 0.0097, 0.0099, 0.0100, 0.0098, 0.0099], dtype=torch.float64,
       requires_grad=True)
in closure, ll=-3479.138234167048
in closure, ll=-3249.6710145073926
--------------------------------------------------------------------------------
epoch: 10
likelihood: -3479.138234167048
sigma_a:
tensor([0.1892], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([3.4212, 3.3263], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 0.1174,  0.0180,  0.0015, -0.1121, -0.0192,  0.0008],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([0.0095, 0.0096, 0.0099, 0.0099, 0.0097, 0.0099], dtype=torch.float64,
       requires_grad=True)
in closure, ll=-3249.6710145073926
in closure, ll=-3143.6122423263114
--------------------------------------------------------------------------------
epoch: 11
likelihood: -3249.6710145073926
sigma_a:
tensor([0.0821], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([3.9339, 3.8210], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 0.1280,  0.0260,  0.0023, -0.1165, -0.0167,  0.0127],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([0.0092, 0.0093, 0.0096, 0.0097, 0.0093, 0.0098], dtype=torch.float64,
       requires_grad=True)
in closure, ll=-3143.6122423263114
in closure, ll=-3082.4024731655104
--------------------------------------------------------------------------------
epoch: 12
likelihood: -3143.6122423263114
sigma_a:
tensor([0.2940], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([4.6809, 4.5417], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 0.1441,  0.0372,  0.0006, -0.1218, -0.0089,  0.0372],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([0.0088, 0.0088, 0.0091, 0.0094, 0.0089, 0.0102], dtype=torch.float64,
       requires_grad=True)
in closure, ll=-3082.4024731655104
in closure, ll=-3079.614375136957
--------------------------------------------------------------------------------
epoch: 13
likelihood: -3082.4024731655104
sigma_a:
tensor([0.2826], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([4.7814, 4.6411], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 0.1470,  0.0391,  0.0003, -0.1229, -0.0077,  0.0412],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([0.0088, 0.0088, 0.0091, 0.0094, 0.0088, 0.0103], dtype=torch.float64,
       requires_grad=True)
in closure, ll=-3079.614375136957
in closure, ll=-3074.662027752058
--------------------------------------------------------------------------------
epoch: 14
likelihood: -3079.614375136957
sigma_a:
tensor([0.2218], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([4.9939, 4.8845], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 0.1688,  0.0525, -0.0080, -0.1285,  0.0097,  0.0866],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([0.0086, 0.0081, 0.0084, 0.0091, 0.0087, 0.0116], dtype=torch.float64,
       requires_grad=True)
in closure, ll=-3074.662027752058
in closure, ll=-3072.09476477654
--------------------------------------------------------------------------------
epoch: 15
likelihood: -3074.662027752058
sigma_a:
tensor([0.1391], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([5.1213, 5.0314], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 0.2063,  0.0747, -0.0286, -0.1357,  0.0481,  0.1778],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([0.0084, 0.0069, 0.0069, 0.0087, 0.0084, 0.0138], dtype=torch.float64,
       requires_grad=True)
in closure, ll=-3072.09476477654
in closure, ll=-3071.4397379422317
--------------------------------------------------------------------------------
epoch: 16
likelihood: -3072.09476477654
sigma_a:
tensor([0.1393], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([5.0593, 4.9661], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 0.2061,  0.0740, -0.0306, -0.1353,  0.0494,  0.1799],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([0.0084, 0.0069, 0.0069, 0.0087, 0.0084, 0.0137], dtype=torch.float64,
       requires_grad=True)
in closure, ll=-3071.4397379422317
in closure, ll=-3070.9911033099515
--------------------------------------------------------------------------------
epoch: 17
likelihood: -3071.4397379422317
sigma_a:
tensor([0.1193], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([4.9529, 4.8498], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 0.2361,  0.0858, -0.0660, -0.1413,  0.0846,  0.2635],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([0.0082, 0.0057, 0.0053, 0.0083, 0.0074, 0.0129], dtype=torch.float64,
       requires_grad=True)
in closure, ll=-3070.9911033099515
in closure, ll=-3071.0227091178754
in closure, ll=-3070.8389080046654
--------------------------------------------------------------------------------
epoch: 18
likelihood: -3070.9911033099515
sigma_a:
tensor([0.1298], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([4.9312, 4.8248], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 0.2343,  0.0841, -0.0669, -0.1411,  0.0829,  0.2597],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([0.0082, 0.0058, 0.0053, 0.0083, 0.0073, 0.0125], dtype=torch.float64,
       requires_grad=True)
in closure, ll=-3070.8389080046654
in closure, ll=-3070.797108670929
--------------------------------------------------------------------------------
epoch: 19
likelihood: -3070.8389080046654
sigma_a:
tensor([0.1315], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([4.9557, 4.8508], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 0.2334,  0.0840, -0.0649, -0.1411,  0.0811,  0.2561],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([0.0082, 0.0058, 0.0054, 0.0083, 0.0073, 0.0125], dtype=torch.float64,
       requires_grad=True)
in closure, ll=-3070.797108670929
in closure, ll=-3070.7551399455488
--------------------------------------------------------------------------------
epoch: 20
likelihood: -3070.797108670929
sigma_a:
tensor([0.1320], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([4.9606, 4.8552], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 0.2407,  0.0871, -0.0727, -0.1434,  0.0872,  0.2728],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([0.0082, 0.0055, 0.0051, 0.0082, 0.0071, 0.0122], dtype=torch.float64,
       requires_grad=True)
in closure, ll=-3070.7551399455488
in closure, ll=-3070.5434173539365
--------------------------------------------------------------------------------
epoch: 21
likelihood: -3070.7551399455488
sigma_a:
tensor([0.1324], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([4.9773, 4.8661], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 0.3121,  0.1172, -0.1496, -0.1663,  0.1461,  0.4362],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([0.0077, 0.0030, 0.0016, 0.0073, 0.0044, 0.0083], dtype=torch.float64,
       requires_grad=True)
in closure, ll=-3070.5434173539365
in closure, ll=-3070.499508174193
--------------------------------------------------------------------------------
epoch: 22
likelihood: -3070.5434173539365
sigma_a:
tensor([0.1317], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([4.9699, 4.8628], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 0.3414,  0.1309, -0.1771, -0.1826,  0.1513,  0.4772],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([0.0075, 0.0022, 0.0006, 0.0069, 0.0034, 0.0065], dtype=torch.float64,
       requires_grad=True)
in closure, ll=-3070.499508174193
in closure, ll=-3070.4002423490588
--------------------------------------------------------------------------------
epoch: 23
likelihood: -3070.499508174193
sigma_a:
tensor([0.1300], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([4.9476, 4.8553], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 0.4254,  0.1724, -0.2493, -0.2393,  0.1396,  0.5577],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([ 6.8641e-03,  9.4420e-05, -1.7961e-03,  6.0707e-03,  9.5573e-04,
         1.3445e-03], dtype=torch.float64, requires_grad=True)
in closure, ll=-3070.4002423490588
in closure, ll=-3070.3016796925226
--------------------------------------------------------------------------------
epoch: 24
likelihood: -3070.4002423490588
sigma_a:
tensor([0.1289], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([4.9285, 4.8532], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 0.5196,  0.2207, -0.3240, -0.3112,  0.1033,  0.6149],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([ 0.0062, -0.0020, -0.0039,  0.0052, -0.0015, -0.0044],
       dtype=torch.float64, requires_grad=True)
in closure, ll=-3070.3016796925226
in closure, ll=-3070.155406014571
--------------------------------------------------------------------------------
epoch: 25
likelihood: -3070.3016796925226
sigma_a:
tensor([0.1289], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([4.9151, 4.8576], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 0.6706,  0.3002, -0.4352, -0.4353,  0.0205,  0.6703],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([ 0.0050, -0.0049, -0.0065,  0.0038, -0.0052, -0.0132],
       dtype=torch.float64, requires_grad=True)
in closure, ll=-3070.155406014571
in closure, ll=-3070.191676031563
in closure, ll=-3070.089907314436
--------------------------------------------------------------------------------
epoch: 26
likelihood: -3070.155406014571
sigma_a:
tensor([0.1292], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([4.9515, 4.8266], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 0.7680,  0.3485, -0.4936, -0.5114, -0.0215,  0.7069],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([ 0.0041, -0.0056, -0.0062,  0.0027, -0.0062, -0.0137],
       dtype=torch.float64, requires_grad=True)
in closure, ll=-3070.089907314436
in closure, ll=-3070.0274424639774
--------------------------------------------------------------------------------
epoch: 27
likelihood: -3070.089907314436
sigma_a:
tensor([0.1311], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([4.9528, 4.8513], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 0.8253,  0.3765, -0.5154, -0.5670, -0.0741,  0.6826],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([ 0.0035, -0.0052, -0.0047,  0.0022, -0.0059, -0.0124],
       dtype=torch.float64, requires_grad=True)
in closure, ll=-3070.0274424639774
in closure, ll=-3070.0224333580645
--------------------------------------------------------------------------------
epoch: 28
likelihood: -3070.0274424639774
sigma_a:
tensor([0.1315], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([4.9589, 4.8565], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 0.8169,  0.3709, -0.5014, -0.5632, -0.0768,  0.6627],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([ 0.0035, -0.0044, -0.0036,  0.0022, -0.0051, -0.0101],
       dtype=torch.float64, requires_grad=True)
in closure, ll=-3070.0224333580645
in closure, ll=-3070.02170829776
--------------------------------------------------------------------------------
epoch: 29
likelihood: -3070.0224333580645
sigma_a:
tensor([0.1314], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([4.9608, 4.8571], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 0.8123,  0.3671, -0.4949, -0.5599, -0.0748,  0.6563],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([ 0.0035, -0.0040, -0.0031,  0.0023, -0.0046, -0.0088],
       dtype=torch.float64, requires_grad=True)
in closure, ll=-3070.02170829776
in closure, ll=-3070.0181485400913
--------------------------------------------------------------------------------
epoch: 30
likelihood: -3070.02170829776
sigma_a:
tensor([0.1314], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([4.9623, 4.8575], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 0.8168,  0.3582, -0.4851, -0.5626, -0.0674,  0.6483],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([ 0.0033, -0.0027, -0.0014,  0.0021, -0.0030, -0.0041],
       dtype=torch.float64, requires_grad=True)
in closure, ll=-3070.0181485400913
in closure, ll=-3069.996661944917
--------------------------------------------------------------------------------
epoch: 31
likelihood: -3070.0181485400913
sigma_a:
tensor([0.1309], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([4.9670, 4.8586], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 0.8856,  0.2925, -0.4347, -0.6073, -0.0097,  0.6084],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([0.0009, 0.0066, 0.0093, 0.0005, 0.0077, 0.0250], dtype=torch.float64,
       requires_grad=True)
in closure, ll=-3069.996661944917
in closure, ll=-3069.9763803012825
--------------------------------------------------------------------------------
epoch: 32
likelihood: -3069.996661944917
sigma_a:
tensor([0.1307], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([4.9671, 4.8586], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 0.9924,  0.2167, -0.3968, -0.6792,  0.0580,  0.5788],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([-0.0021,  0.0157,  0.0183, -0.0015,  0.0181,  0.0496],
       dtype=torch.float64, requires_grad=True)
in closure, ll=-3069.9763803012825
in closure, ll=-3069.943489273346
--------------------------------------------------------------------------------
epoch: 33
likelihood: -3069.9763803012825
sigma_a:
tensor([0.1306], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([4.9650, 4.8581], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 1.1877,  0.0779, -0.3488, -0.8149,  0.1739,  0.5345],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([-0.0070,  0.0253,  0.0240, -0.0049,  0.0290,  0.0659],
       dtype=torch.float64, requires_grad=True)
in closure, ll=-3069.943489273346
in closure, ll=-3069.9481480816
in closure, ll=-3069.916917346895
--------------------------------------------------------------------------------
epoch: 34
likelihood: -3069.943489273346
sigma_a:
tensor([0.1302], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([4.9743, 4.8604], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 1.3574, -0.1012, -0.2522, -0.9408,  0.3047,  0.4504],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([-0.0088,  0.0111,  0.0072, -0.0059,  0.0131,  0.0215],
       dtype=torch.float64, requires_grad=True)
in closure, ll=-3069.916917346895
in closure, ll=-3069.893557861239
--------------------------------------------------------------------------------
epoch: 35
likelihood: -3069.916917346895
sigma_a:
tensor([0.1305], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([4.9640, 4.8578], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 1.5155, -0.1856, -0.2579, -1.0576,  0.3707,  0.4556],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([-0.0100,  0.0074,  0.0060, -0.0069,  0.0087,  0.0174],
       dtype=torch.float64, requires_grad=True)
in closure, ll=-3069.893557861239
in closure, ll=-3069.889502180957
--------------------------------------------------------------------------------
epoch: 36
likelihood: -3069.893557861239
sigma_a:
tensor([0.1306], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([4.9592, 4.8567], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 1.5397, -0.1923, -0.2743, -1.0792,  0.3719,  0.4708],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([-0.0089,  0.0007,  0.0010, -0.0061,  0.0009,  0.0032],
       dtype=torch.float64, requires_grad=True)
in closure, ll=-3069.889502180957
in closure, ll=-3069.889302999934
--------------------------------------------------------------------------------
epoch: 37
likelihood: -3069.889502180957
sigma_a:
tensor([0.1306], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([4.9589, 4.8566], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 1.5288, -0.1855, -0.2789, -1.0734,  0.3638,  0.4756],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([-0.0078, -0.0007, -0.0001, -0.0054, -0.0007, -0.0002],
       dtype=torch.float64, requires_grad=True)
in closure, ll=-3069.889302999934
in closure, ll=-3069.889215849931
--------------------------------------------------------------------------------
epoch: 38
likelihood: -3069.889302999934
sigma_a:
tensor([0.1306], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([4.9589, 4.8566], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 1.5235, -0.1840, -0.2793, -1.0717,  0.3597,  0.4780],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([-0.0067, -0.0008, -0.0004, -0.0046, -0.0009, -0.0011],
       dtype=torch.float64, requires_grad=True)
in closure, ll=-3069.889215849931
in closure, ll=-3069.8890746285097
--------------------------------------------------------------------------------
epoch: 39
likelihood: -3069.889215849931
sigma_a:
tensor([0.1306], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([4.9590, 4.8565], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 1.5172, -0.1853, -0.2774, -1.0726,  0.3538,  0.4823],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([-0.0037, -0.0005, -0.0005, -0.0025, -0.0007, -0.0017],
       dtype=torch.float64, requires_grad=True)
in closure, ll=-3069.8890746285097
in closure, ll=-3069.889009183084
--------------------------------------------------------------------------------
epoch: 40
likelihood: -3069.8890746285097
sigma_a:
tensor([0.1306], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([4.9590, 4.8565], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 1.5186, -0.1894, -0.2739, -1.0768,  0.3530,  0.4844],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([-1.6956e-03, -8.9262e-05, -3.5135e-04, -1.0405e-03, -1.9095e-04,
        -1.1422e-03], dtype=torch.float64, requires_grad=True)
in closure, ll=-3069.889009183084
in closure, ll=-3069.8889923582547
--------------------------------------------------------------------------------
epoch: 41
likelihood: -3069.889009183084
sigma_a:
tensor([0.1306], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([4.9590, 4.8566], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 1.5225, -0.1929, -0.2715, -1.0802,  0.3546,  0.4844],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([-8.4603e-04,  1.1849e-04, -6.3958e-05, -4.6012e-04,  8.4803e-05,
        -2.0468e-04], dtype=torch.float64, requires_grad=True)
in closure, ll=-3069.8889923582547
in closure, ll=-3069.888991223574
--------------------------------------------------------------------------------
epoch: 42
likelihood: -3069.8889923582547
sigma_a:
tensor([0.1306], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([4.9590, 4.8566], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 1.5236, -0.1935, -0.2712, -1.0807,  0.3551,  0.4842],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([-7.9267e-04,  1.0683e-04,  1.8060e-06, -4.3508e-04,  9.3544e-05,
         1.2912e-05], dtype=torch.float64, requires_grad=True)
in closure, ll=-3069.888991223574
in closure, ll=-3069.8889907353246
--------------------------------------------------------------------------------
epoch: 43
likelihood: -3069.888991223574
sigma_a:
tensor([0.1306], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([4.9590, 4.8566], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 1.5242, -0.1938, -0.2711, -1.0807,  0.3554,  0.4840],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([-7.4806e-04,  6.6812e-05,  2.9122e-05, -4.1587e-04,  6.5253e-05,
         1.0576e-04], dtype=torch.float64, requires_grad=True)
in closure, ll=-3069.8889907353246
in closure, ll=-3069.888989847685
--------------------------------------------------------------------------------
epoch: 44
likelihood: -3069.8889907353246
sigma_a:
tensor([0.1306], dtype=torch.float64, requires_grad=True)
sqrt_diag_R:
tensor([4.9590, 4.8566], dtype=torch.float64, requires_grad=True)
m0:
tensor([ 1.5248, -0.1940, -0.2710, -1.0805,  0.3555,  0.4839],
       dtype=torch.float64, requires_grad=True)
sqrt_diag_V0:
tensor([-5.8176e-04, -2.9934e-05,  5.7180e-05, -3.2573e-04, -1.3763e-05,
         2.0292e-04], dtype=torch.float64, requires_grad=True)

EM

Code for lds.learning.em_SS_tracking

V0_0 = np.diag(sqrt_diag_V0_0**2)
R0 = np.diag(sqrt_diag_R_0)
Qe_reg_param = 1e-5
Qe_regularized = Qe + Qe_reg_param*np.eye(Qe.shape[0])
optim_res_em = lds.learning.em_SS_tracking(
    y=y, B=B, sigma_a0=sigma_a0,
    Qe=Qe_regularized, Z=Z, R_0=R0, m0_0=m0_0, V0_0=V0_0,
    vars_to_estimate=em_vars_to_estimate, max_iter=em_max_iter)

LogLike[0000]=-4180.626488
sigma_a=0.250000
R:
[[4.95902963 0.        ]
 [0.         4.85657707]]
m0:
[ 1.52483735 -0.19400139 -0.27101684 -1.0805486   0.35547295  0.48393198]
V0:
[[3.38439500e-07 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00]
 [0.00000000e+00 8.96045095e-10 0.00000000e+00 0.00000000e+00
  0.00000000e+00 0.00000000e+00]
 [0.00000000e+00 0.00000000e+00 3.26954476e-09 0.00000000e+00
  0.00000000e+00 0.00000000e+00]
 [0.00000000e+00 0.00000000e+00 0.00000000e+00 1.06096828e-07
  0.00000000e+00 0.00000000e+00]
 [0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  1.89408339e-10 0.00000000e+00]
 [0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
  0.00000000e+00 4.11771861e-08]]
LogLike[0001]=-3074.833889
sigma_a=0.250306
R:
[[23.52834676 -1.42643785]
 [-1.42643785 22.85473798]]
m0:
[ 1.52483709 -0.19400139 -0.27101685 -1.08054868  0.35547295  0.48393197]
V0:
[[ 3.38439078e-07 -1.07537700e-15 -1.79132169e-15  0.00000000e+00
   0.00000000e+00  0.00000000e+00]
 [-1.07537700e-15  8.96045091e-10 -9.13479878e-18  0.00000000e+00
   0.00000000e+00  0.00000000e+00]
 [-1.79132169e-15 -9.13479878e-18  3.26954473e-09  0.00000000e+00
   0.00000000e+00  0.00000000e+00]
 [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  1.06096786e-07
  -7.22467799e-17 -7.14398188e-15]
 [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 -7.22467799e-17
   1.89408339e-10 -2.44796462e-17]
 [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 -7.14398188e-15
  -2.44796462e-17  4.11771810e-08]]
LogLike[0002]=-3074.531154
sigma_a=0.249707
R:
[[24.39082997 -1.4346038 ]
 [-1.4346038  23.48301459]]
m0:
[ 1.52483706 -0.19400139 -0.27101685 -1.08054869  0.35547295  0.48393196]
V0:
[[ 3.38438961e-07 -1.46119981e-15 -2.63358338e-15 -1.88674094e-15
  -3.34555484e-18 -3.20054874e-16]
 [-1.46119981e-15  8.96045089e-10 -1.46949664e-17 -4.96158313e-18
  -1.21362511e-20 -1.38679806e-18]
 [-2.63358338e-15 -1.46949664e-17  3.26954470e-09 -7.96666203e-18
  -2.32762535e-20 -3.02078859e-18]
 [-1.88674094e-15 -4.96158310e-18 -7.96666203e-18  1.06096774e-07
  -9.83090167e-17 -1.05167197e-14]
 [-3.34555484e-18 -1.21362512e-20 -2.32762535e-20 -9.83090163e-17
   1.89408339e-10 -3.94202915e-17]
 [-3.20054874e-16 -1.38679806e-18 -3.02078859e-18 -1.05167197e-14
  -3.94202915e-17  4.11771770e-08]]
LogLike[0003]=-3074.492912
sigma_a=0.249071
R:
[[24.4203829  -1.43321921]
 [-1.43321921 23.50080856]]
m0:
[ 1.52483702 -0.19400139 -0.27101685 -1.08054871  0.35547295  0.48393196]
V0:
[[ 3.38438847e-07 -1.83853575e-15 -3.46319567e-15 -3.67925866e-15
  -6.54341534e-18 -6.27953807e-16]
 [-1.83853576e-15  8.96045087e-10 -2.02091127e-17 -9.70412956e-18
  -2.38088295e-20 -2.72915351e-18]
 [-3.46319567e-15 -2.02091127e-17  3.26954468e-09 -1.56307423e-17
  -4.58065740e-20 -5.96331393e-18]
 [-3.67925866e-15 -9.70412951e-18 -1.56307423e-17  1.06096762e-07
  -1.23947975e-16 -1.38532160e-14]
 [-6.54341531e-18 -2.38088299e-20 -4.58065740e-20 -1.23947975e-16
   1.89408339e-10 -5.42795448e-17]
 [-6.27953807e-16 -2.72915351e-18 -5.96331393e-18 -1.38532160e-14
  -5.42795448e-17  4.11771729e-08]]
LogLike[0004]=-3074.457381
sigma_a=0.248476
R:
[[24.42215852 -1.43295551]
 [-1.43295551 23.50144452]]
m0:
[ 1.52483699 -0.19400139 -0.27101685 -1.08054872  0.35547295  0.48393196]
V0:
[[ 3.38438734e-07 -2.21622123e-15 -4.29448786e-15 -5.46840285e-15
  -9.73850179e-18 -9.35916283e-16]
 [-2.21622124e-15  8.96045085e-10 -2.57402472e-17 -1.44425615e-17
  -3.54833662e-20 -4.07316686e-18]
 [-4.29448786e-15 -2.57402472e-17  3.26954465e-09 -2.32964027e-17
  -6.83647201e-20 -8.91258780e-18]
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 [-9.35916283e-16 -4.07316686e-18 -8.91258780e-18 -1.71972093e-14
  -6.91867512e-17  4.11771689e-08]]
LogLike[0005]=-3074.421156
sigma_a=0.247869
R:
[[24.42296295 -1.43278039]
 [-1.43278039 23.5015904 ]]
m0:
[ 1.52483696 -0.19400139 -0.27101685 -1.08054874  0.35547295  0.48393196]
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[[ 3.38438620e-07 -2.59450271e-15 -5.12779375e-15 -7.25854739e-15
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 [-7.25854739e-15 -1.91874668e-17 -3.09790817e-17  1.06096739e-07
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  -8.41423936e-17  4.11771648e-08]]
LogLike[0006]=-3074.384419
sigma_a=0.247253
R:
[[24.42375132 -1.43260586]
 [-1.43260586 23.50172621]]
m0:
[ 1.52483692 -0.19400139 -0.27101685 -1.08054876  0.35547295  0.48393196]
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[[ 3.38438506e-07 -2.97340493e-15 -5.96318014e-15 -9.04993691e-15
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  -9.91478156e-17  4.11771608e-08]]
LogLike[0007]=-3074.347587
sigma_a=0.246636
R:
[[24.4245516  -1.43242867]
 [-1.43242867 23.50186493]]
m0:
[ 1.52483689 -0.19400139 -0.27101685 -1.08054877  0.35547295  0.48393195]
V0:
[[ 3.38438393e-07 -3.35293964e-15 -6.80068777e-15 -1.08426005e-14
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  -1.14204025e-16  4.11771567e-08]]
LogLike[0008]=-3074.311953
sigma_a=0.246038
R:
[[24.42535601 -1.43225064]
 [-1.43225064 23.50200547]]
m0:
[ 1.52483686 -0.19400139 -0.27101685 -1.08054879  0.35547295  0.48393195]
V0:
[[ 3.38438279e-07 -3.73311117e-15 -7.64033312e-15 -1.26365428e-14
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LogLike[0009]=-3074.276212
sigma_a=0.245439
R:
[[24.42613692 -1.43207785]
 [-1.43207785 23.50214296]]
m0:
[ 1.52483683 -0.19400139 -0.27101685 -1.0805488   0.35547295  0.48393195]
V0:
[[ 3.38438165e-07 -4.11390116e-15 -8.48205684e-15 -1.44317162e-14
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 [-1.44317162e-14 -3.82397780e-17 -6.18949682e-17  1.06096693e-07
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LogLike[0010]=-3074.241232
sigma_a=0.244852
R:
[[24.42692096 -1.43190443]
 [-1.43190443 23.50228209]]
m0:
[ 1.52483679 -0.19400139 -0.27101685 -1.08054882  0.35547295  0.48393195]
V0:
[[ 3.38438051e-07 -4.49531444e-15 -9.32587642e-15 -1.62281386e-14
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 [-1.62281386e-14 -4.30209653e-17 -6.96701567e-17  1.06096681e-07
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LogLike[0011]=-3074.206421
sigma_a=0.244268
R:
[[24.42769054 -1.43173427]
 [-1.43173427 23.50241969]]
m0:
[ 1.52483676 -0.19400139 -0.27101685 -1.08054883  0.35547295  0.48393195]
V0:
[[ 3.38437936e-07 -4.87734012e-15 -1.01717573e-14 -1.80257809e-14
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  -1.74933496e-16  4.11771401e-08]]
LogLike[0012]=-3074.170564
sigma_a=0.243666
R:
[[24.42845762 -1.43156471]
 [-1.43156471 23.50255789]]
m0:
[ 1.52483673 -0.19400139 -0.27101685 -1.08054885  0.35547295  0.48393194]
V0:
[[ 3.38437822e-07 -5.25997795e-15 -1.10197001e-14 -1.98246458e-14
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  -2.51435540e-19 -3.29396911e-17]
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   1.89408338e-10 -1.90240206e-16]
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  -1.90240206e-16  4.11771359e-08]]
LogLike[0013]=-3074.135584
sigma_a=0.243079
R:
[[24.42924855 -1.43138996]
 [-1.43138996 23.50270149]]
m0:
[ 1.5248367  -0.19400139 -0.27101685 -1.08054886  0.35547295  0.48393194]
V0:
[[ 3.38437708e-07 -5.64324935e-15 -1.18697783e-14 -2.16247842e-14
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  -1.41783300e-19 -1.63636431e-17]
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  -2.74650108e-19 -3.59980751e-17]
 [-2.16247842e-14 -5.74073085e-17 -9.31051512e-17  1.06096647e-07
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   1.89408338e-10 -2.05598291e-16]
 [-3.74043614e-15 -1.63636431e-17 -3.59980751e-17 -4.76722776e-14
  -2.05598291e-16  4.11771317e-08]]
LogLike[0014]=-3074.099826
sigma_a=0.242479
R:
[[24.43002316 -1.43121884]
 [-1.43121884 23.5028432 ]]
m0:
[ 1.52483667 -0.19400139 -0.27101685 -1.08054888  0.35547295  0.48393194]
V0:
[[ 3.38437593e-07 -6.02714108e-15 -1.27219498e-14 -2.34261545e-14
  -4.19525688e-17 -4.05575037e-15]
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 [-2.34261545e-14 -6.22171948e-17 -1.00953792e-16  1.06096635e-07
  -4.08666884e-16 -5.11007557e-14]
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   1.89408338e-10 -2.21006793e-16]
 [-4.05575037e-15 -1.77511484e-17 -3.90687268e-17 -5.11007557e-14
  -2.21006793e-16  4.11771275e-08]]
LogLike[0015]=-3074.065550
sigma_a=0.241903
R:
[[24.43081553 -1.43104387]
 [-1.43104387 23.50298928]]
m0:
[ 1.52483664 -0.19400139 -0.27101685 -1.08054889  0.35547295  0.48393194]
V0:
[[ 3.38437479e-07 -6.41167007e-15 -1.35762728e-14 -2.52288013e-14
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  -1.65710884e-19 -1.91431690e-17]
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  -3.21302124e-19 -4.21520243e-17]
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   1.89408338e-10 -2.36467148e-16]
 [-4.37182581e-15 -1.91431690e-17 -4.21520243e-17 -5.45379355e-14
  -2.36467148e-16  4.11771233e-08]]
LogLike[0016]=-3074.030983
sigma_a=0.241323
R:
[[24.43157828 -1.43087547]
 [-1.43087547 23.50313095]]
m0:
[ 1.5248366  -0.19400139 -0.27101685 -1.08054891  0.35547295  0.48393194]
V0:
[[ 3.38437364e-07 -6.79681203e-15 -1.44326679e-14 -2.70326585e-14
  -4.84538523e-17 -4.68863170e-15]
 [-6.79681204e-15  8.96045063e-10 -9.35581233e-17 -7.18588291e-17
  -1.77716235e-19 -2.05395308e-17]
 [-1.44326679e-14 -9.35581233e-17  3.26954434e-09 -1.16707147e-16
  -3.44738886e-19 -4.52474980e-17]
 [-2.70326585e-14 -7.18588292e-17 -1.16707147e-16  1.06096612e-07
  -4.60991084e-16 -5.79834985e-14]
 [-4.84538523e-17 -1.77716235e-19 -3.44738886e-19 -4.60991083e-16
   1.89408338e-10 -2.51977502e-16]
 [-4.68863170e-15 -2.05395308e-17 -4.52474980e-17 -5.79834985e-14
  -2.51977502e-16  4.11771190e-08]]
LogLike[0017]=-3073.996650
sigma_a=0.240746
R:
[[24.43234788 -1.43070562]
 [-1.43070562 23.50327499]]
m0:
[ 1.52483657 -0.19400139 -0.27101685 -1.08054892  0.35547295  0.48393194]
V0:
[[ 3.38437249e-07 -7.18257525e-15 -1.52911643e-14 -2.88377543e-14
  -5.17117329e-17 -5.00618025e-15]
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  -1.89749367e-19 -2.19403062e-17]
 [-1.52911643e-14 -9.93311705e-17  3.26954431e-09 -1.24611399e-16
  -3.68249726e-19 -4.83553548e-17]
 [-2.88377543e-14 -7.66903812e-17 -1.24611399e-16  1.06096600e-07
  -4.87216939e-16 -6.14375601e-14]
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   1.89408338e-10 -2.67538581e-16]
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  -2.67538581e-16  4.11771147e-08]]
LogLike[0018]=-3073.962510
sigma_a=0.240172
R:
[[24.43311423 -1.43053653]
 [-1.43053653 23.50341949]]
m0:
[ 1.52483654 -0.19400139 -0.27101685 -1.08054894  0.35547295  0.48393193]
V0:
[[ 3.38437134e-07 -7.56895807e-15 -1.61517582e-14 -3.06440809e-14
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  -2.01810207e-19 -2.33454883e-17]
 [-1.61517582e-14 -1.05122971e-16  3.26954428e-09 -1.32534088e-16
  -3.91834529e-19 -5.14755876e-17]
 [-3.06440809e-14 -8.15291036e-17 -1.32534088e-16  1.06096588e-07
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   1.89408338e-10 -2.83150342e-16]
 [-5.32446954e-15 -2.33454883e-17 -5.14755876e-17 -6.49001059e-14
  -2.83150342e-16  4.11771105e-08]]
LogLike[0019]=-3073.928850
sigma_a=0.239606
R:
[[24.43387786 -1.43036809]
 [-1.43036809 23.50356455]]
m0:
[ 1.52483651 -0.19400139 -0.27101685 -1.08054895  0.35547295  0.48393193]
V0:
[[ 3.38437019e-07 -7.95595968e-15 -1.70144486e-14 -3.24516356e-14
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  -2.13898739e-19 -2.47550782e-17]
 [-1.70144486e-14 -1.10933530e-16  3.26954426e-09 -1.40475203e-16
  -4.15493313e-19 -5.46082096e-17]
 [-3.24516356e-14 -8.63749866e-17 -1.40475203e-16  1.06096577e-07
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   1.89408338e-10 -2.98812800e-16]
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  -2.98812800e-16  4.11771062e-08]]
LogLike[0020]=-3073.895382
sigma_a=0.239043
R:
[[24.43463253 -1.43020166]
 [-1.43020166 23.50370897]]
m0:
[ 1.52483648 -0.19400139 -0.27101685 -1.08054897  0.35547295  0.48393193]
V0:
[[ 3.38436904e-07 -8.34357391e-15 -1.78792165e-14 -3.42604031e-14
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   1.89408338e-10 -3.14525539e-16]
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  -3.14525539e-16  4.11771018e-08]]
LogLike[0021]=-3073.861407
sigma_a=0.238471
R:
[[24.43538426 -1.43003593]
 [-1.43003593 23.50385388]]
m0:
[ 1.52483645 -0.19400139 -0.27101685 -1.08054898  0.35547295  0.48393193]
V0:
[[ 3.38436789e-07 -8.73179996e-15 -1.87460606e-14 -3.60703828e-14
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LogLike[0022]=-3073.827918
sigma_a=0.237907
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[[24.43614843 -1.42986751]
 [-1.42986751 23.5040023 ]]
m0:
[ 1.52483642 -0.19400139 -0.27101685 -1.080549    0.35547295  0.48393193]
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[[ 3.38436674e-07 -9.12064996e-15 -1.96150236e-14 -3.78816032e-14
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LogLike[0023]=-3073.796367
sigma_a=0.237376
R:
[[24.43690396 -1.42970102]
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m0:
[ 1.52483639 -0.19400139 -0.27101685 -1.08054901  0.35547295  0.48393193]
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[[ 3.38436559e-07 -9.51011742e-15 -2.04860856e-14 -3.96940430e-14
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LogLike[0024]=-3073.764364
sigma_a=0.236837
R:
[[24.43761835 -1.42954362]
 [-1.42954362 23.50429084]]
m0:
[ 1.52483636 -0.19400139 -0.27101685 -1.08054903  0.35547295  0.48393192]
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[[ 3.38436443e-07 -9.90016869e-15 -2.13591344e-14 -4.15076230e-14
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LogLike[0025]=-3073.732324
sigma_a=0.236297
R:
[[24.43834261 -1.4293841 ]
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m0:
[ 1.52483633 -0.19400139 -0.27101685 -1.08054904  0.35547295  0.48393192]
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[[ 3.38436328e-07 -1.02908151e-14 -2.22342093e-14 -4.33223828e-14
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LogLike[0026]=-3073.699692
sigma_a=0.235746
R:
[[24.43906945 -1.42922405]
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m0:
[ 1.5248363  -0.19400139 -0.27101685 -1.08054906  0.35547295  0.48393192]
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[[ 3.38436212e-07 -1.06820599e-14 -2.31113228e-14 -4.51383251e-14
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LogLike[0027]=-3073.667080
sigma_a=0.235196
R:
[[24.43981078 -1.42906084]
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m0:
[ 1.52483627 -0.19400139 -0.27101685 -1.08054907  0.35547295  0.48393192]
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[[ 3.38436097e-07 -1.10739168e-14 -2.39905232e-14 -4.69554804e-14
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LogLike[0028]=-3073.634857
sigma_a=0.234652
R:
[[24.44055361 -1.42889733]
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m0:
[ 1.52483624 -0.19400139 -0.27101685 -1.08054909  0.35547295  0.48393192]
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[[ 3.38435981e-07 -1.14663880e-14 -2.48718197e-14 -4.87738473e-14
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LogLike[0029]=-3073.603350
sigma_a=0.234120
R:
[[24.44128937 -1.4287354 ]
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m0:
[ 1.52483621 -0.19400139 -0.27101685 -1.0805491   0.35547295  0.48393192]
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[[ 3.38435865e-07 -1.18594686e-14 -2.57551977e-14 -5.05934124e-14
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LogLike[0030]=-3073.570751
sigma_a=0.233570
R:
[[24.4420105  -1.42857672]
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m0:
[ 1.52483618 -0.19400139 -0.27101685 -1.08054912  0.35547295  0.48393191]
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[[ 3.38435749e-07 -1.22531475e-14 -2.66406213e-14 -5.24141501e-14
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LogLike[0031]=-3073.539574
sigma_a=0.233043
R:
[[24.44275676 -1.42841256]
 [-1.42841256 23.50533249]]
m0:
[ 1.52483615 -0.19400139 -0.27101685 -1.08054913  0.35547295  0.48393191]
V0:
[[ 3.38435633e-07 -1.26474487e-14 -2.75281729e-14 -5.42361205e-14
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LogLike[0032]=-3073.508073
sigma_a=0.232510
R:
[[24.44347369 -1.42825485]
 [-1.42825485 23.50548195]]
m0:
[ 1.52483613 -0.19400139 -0.27101684 -1.08054915  0.35547295  0.48393191]
V0:
[[ 3.38435517e-07 -1.30423470e-14 -2.84177691e-14 -5.60592539e-14
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LogLike[0033]=-3073.475946
sigma_a=0.231967
R:
[[24.44419829 -1.4280955 ]
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m0:
[ 1.5248361  -0.19400139 -0.27101684 -1.08054916  0.35547295  0.48393191]
V0:
[[ 3.38435401e-07 -1.34378516e-14 -2.93094424e-14 -5.78835806e-14
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LogLike[0034]=-3073.445184
sigma_a=0.231446
R:
[[24.44493849 -1.42793275]
 [-1.42793275 23.50579062]]
m0:
[ 1.52483607 -0.19400139 -0.27101684 -1.08054918  0.35547295  0.48393191]
V0:
[[ 3.38435285e-07 -1.38339772e-14 -3.02032451e-14 -5.97091316e-14
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LogLike[0035]=-3073.414594
sigma_a=0.230928
R:
[[24.44565014 -1.42777627]
 [-1.42777627 23.50594213]]
m0:
[ 1.52483604 -0.19400139 -0.27101684 -1.08054919  0.35547295  0.48393191]
V0:
[[ 3.38435168e-07 -1.42306997e-14 -3.10990964e-14 -6.15358424e-14
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LogLike[0036]=-3073.383115
sigma_a=0.230395
R:
[[24.44635836 -1.42762058]
 [-1.42762058 23.50609397]]
m0:
[ 1.52483601 -0.19400139 -0.27101684 -1.0805492   0.35547295  0.48393191]
V0:
[[ 3.38435052e-07 -1.46280186e-14 -3.19969957e-14 -6.33637201e-14
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LogLike[0037]=-3073.352708
sigma_a=0.229880
R:
[[24.44708777 -1.42746027]
 [-1.42746027 23.50625145]]
m0:
[ 1.52483598 -0.19400139 -0.27101684 -1.08054922  0.35547295  0.4839319 ]
V0:
[[ 3.38434935e-07 -1.50259540e-14 -3.28970137e-14 -6.51928124e-14
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LogLike[0038]=-3073.321583
sigma_a=0.229352
R:
[[24.44779518 -1.42730479]
 [-1.42730479 23.50640522]]
m0:
[ 1.52483596 -0.19400139 -0.27101684 -1.08054923  0.35547295  0.4839319 ]
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LogLike[0050]=-3072.970198
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LogLike[0051]=-3072.942055
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LogLike[0052]=-3072.913369
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LogLike[0053]=-3072.884214
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LogLike[0054]=-3072.854905
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LogLike[0055]=-3072.827188
sigma_a=0.220918
R:
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LogLike[0080]=-3072.180467
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LogLike[0081]=-3072.156991
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[[24.47618265 -1.42106331]
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m0:
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LogLike[0082]=-3072.133480
sigma_a=0.208871
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m0:
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LogLike[0083]=-3072.109565
sigma_a=0.208449
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[[24.47737185 -1.42080083]
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m0:
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LogLike[0084]=-3072.086218
sigma_a=0.208038
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[[24.47797832 -1.42066692]
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m0:
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LogLike[0085]=-3072.064161
sigma_a=0.207648
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[[24.47857227 -1.42053571]
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m0:
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LogLike[0086]=-3072.042127
sigma_a=0.207258
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[[24.47913505 -1.42041133]
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m0:
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LogLike[0087]=-3072.019763
sigma_a=0.206862
R:
[[24.47969724 -1.42028706]
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m0:
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LogLike[0088]=-3071.996488
sigma_a=0.206450
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[[24.48026857 -1.42016074]
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m0:
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LogLike[0098]=-3071.778730
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m0:
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LogLike[0099]=-3071.757364
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m0:
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LogLike[0100]=-3071.735570
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LogLike[0101]=-3071.714701
sigma_a=0.201412
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m0:
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LogLike[0102]=-3071.693893
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[[24.48817554 -1.41840706]
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m0:
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LogLike[0103]=-3071.673568
sigma_a=0.200670
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[[24.48872261 -1.41828531]
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m0:
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LogLike[0104]=-3071.653295
sigma_a=0.200303
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m0:
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LogLike[0105]=-3071.632756
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m0:
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LogLike[0112]=-3071.493329
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LogLike[0113]=-3071.474225
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LogLike[0114]=-3071.455648
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LogLike[0115]=-3071.436689
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m0:
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LogLike[0116]=-3071.416808
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LogLike[0117]=-3071.398599
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LogLike[0118]=-3071.379413
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LogLike[0119]=-3071.359601
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LogLike[0120]=-3071.342228
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LogLike[0121]=-3071.323056
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LogLike[0122]=-3071.304438
sigma_a=0.193903
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LogLike[0134]=-3071.099388
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LogLike[0135]=-3071.083769
sigma_a=0.189752
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LogLike[0136]=-3071.068112
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LogLike[0137]=-3071.051807
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LogLike[0138]=-3071.035653
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LogLike[0139]=-3071.020611
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LogLike[0170]=-3070.575788
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LogLike[0171]=-3070.562962
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LogLike[0172]=-3070.550986
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LogLike[0206]=-3070.160697
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LogLike[0215]=-3070.075455
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LogLike[0216]=-3070.066372
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LogLike[0217]=-3070.057388
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LogLike[0218]=-3070.049805
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LogLike[0219]=-3070.041631
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m0:
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LogLike[0220]=-3070.031927
sigma_a=0.168021
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LogLike[0221]=-3070.023973
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LogLike[0222]=-3070.015505
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LogLike[0223]=-3070.006751
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LogLike[0285]=-3069.591981
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LogLike[0286]=-3069.586778
sigma_a=0.156688
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LogLike[0287]=-3069.581809
sigma_a=0.156546
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LogLike[0288]=-3069.576765
sigma_a=0.156400
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LogLike[0289]=-3069.571868
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LogLike[0293]=-3069.554405
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LogLike[0294]=-3069.549733
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LogLike[0295]=-3069.544730
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LogLike[0298]=-3069.529395
sigma_a=0.155009
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LogLike[0299]=-3069.525048
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m0:
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LogLike[0300]=-3069.519725
sigma_a=0.154719
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m0:
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LogLike[0301]=-3069.515097
sigma_a=0.154579
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m0:
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LogLike[0302]=-3069.510924
sigma_a=0.154453
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m0:
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LogLike[0303]=-3069.506941
sigma_a=0.154331
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m0:
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LogLike[0304]=-3069.502784
sigma_a=0.154205
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m0:
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LogLike[0305]=-3069.498239
sigma_a=0.154065
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m0:
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LogLike[0306]=-3069.494042
sigma_a=0.153936
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m0:
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LogLike[0390]=-3069.253756
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[ 1.52483161 -0.1940014  -0.27101679 -1.08055206  0.35547294  0.48393204]
V0:
[[ 3.38389676e-07 -1.85320818e-13 -4.59773979e-13 -7.65625162e-13
  -1.53235009e-15 -1.67009514e-13]
 [-1.85320818e-13  8.96044070e-10 -3.44409381e-15 -2.27249134e-15
  -6.30517145e-18 -8.22339418e-16]
 [-4.59773979e-13 -3.44409381e-15  3.26952693e-09 -4.15700830e-15
  -1.38023549e-17 -2.04754666e-15]
 [-7.65625162e-13 -2.27249134e-15 -4.15700830e-15  1.06091762e-07
  -1.26183496e-14 -1.85207061e-12]
 [-1.53235009e-15 -6.30517145e-18 -1.38023549e-17 -1.26183496e-14
   1.89408293e-10 -9.29085053e-15]
 [-1.67009514e-13 -8.22339418e-16 -2.04754666e-15 -1.85207061e-12
  -9.29085053e-15  4.11743401e-08]]
LogLike[0391]=-3069.251487
sigma_a=0.145248
R:
[[24.57000523 -1.3981788 ]
 [-1.3981788  23.56219234]]
m0:
[ 1.5248316  -0.1940014  -0.27101679 -1.08055206  0.35547294  0.48393204]
V0:
[[ 3.38389540e-07 -1.85862768e-13 -4.61212468e-13 -7.67712734e-13
  -1.53681490e-15 -1.67529764e-13]
 [-1.85862768e-13  8.96044066e-10 -3.45555914e-15 -2.27911260e-15
  -6.32477349e-18 -8.25064285e-16]
 [-4.61212468e-13 -3.45555914e-15  3.26952687e-09 -4.16995757e-15
  -1.38480903e-17 -2.05475544e-15]
 [-7.67712734e-13 -2.27911260e-15 -4.16995757e-15  1.06091749e-07
  -1.26552761e-14 -1.85786784e-12]
 [-1.53681490e-15 -6.32477349e-18 -1.38480903e-17 -1.26552761e-14
   1.89408292e-10 -9.32178744e-15]
 [-1.67529764e-13 -8.25064285e-16 -2.05475544e-15 -1.85786784e-12
  -9.32178744e-15  4.11743300e-08]]
LogLike[0392]=-3069.249495
sigma_a=0.145161
R:
[[24.57014151 -1.39813802]
 [-1.39813802 23.56231826]]
m0:
[ 1.5248316  -0.1940014  -0.27101679 -1.08055207  0.35547294  0.48393204]
V0:
[[ 3.38389403e-07 -1.86404965e-13 -4.62651951e-13 -7.69800746e-13
  -1.54128166e-15 -1.68050365e-13]
 [-1.86404965e-13  8.96044063e-10 -3.46703500e-15 -2.28573675e-15
  -6.34438863e-18 -8.27791616e-16]
 [-4.62651951e-13 -3.46703500e-15  3.26952680e-09 -4.18291559e-15
  -1.38938671e-17 -2.06197243e-15]
 [-7.69800746e-13 -2.28573676e-15 -4.18291559e-15  1.06091735e-07
  -1.26922196e-14 -1.86366908e-12]
 [-1.54128166e-15 -6.34438863e-18 -1.38938671e-17 -1.26922196e-14
   1.89408292e-10 -9.35275276e-15]
 [-1.68050365e-13 -8.27791616e-16 -2.06197243e-15 -1.86366908e-12
  -9.35275276e-15  4.11743200e-08]]
LogLike[0393]=-3069.247378
sigma_a=0.145068
R:
[[24.5702635  -1.39810139]
 [-1.39810139 23.56243121]]
m0:
[ 1.52483159 -0.1940014  -0.27101679 -1.08055207  0.35547294  0.48393204]
V0:
[[ 3.38389267e-07 -1.86947381e-13 -4.64092312e-13 -7.71889107e-13
  -1.54575007e-15 -1.68571267e-13]
 [-1.86947381e-13  8.96044060e-10 -3.47852015e-15 -2.29236335e-15
  -6.36401500e-18 -8.30521078e-16]
 [-4.64092312e-13 -3.47852015e-15  3.26952674e-09 -4.19588109e-15
  -1.39396797e-17 -2.06919656e-15]
 [-7.71889107e-13 -2.29236335e-15 -4.19588109e-15  1.06091721e-07
  -1.27291778e-14 -1.86947385e-12]
 [-1.54575007e-15 -6.36401500e-18 -1.39396797e-17 -1.27291779e-14
   1.89408292e-10 -9.38374316e-15]
 [-1.68571267e-13 -8.30521078e-16 -2.06919656e-15 -1.86947385e-12
  -9.38374316e-15  4.11743099e-08]]
LogLike[0394]=-3069.244544
sigma_a=0.144943
R:
[[24.57039308 -1.39806248]
 [-1.39806248 23.56255143]]
m0:
[ 1.52483159 -0.1940014  -0.27101679 -1.08055207  0.35547294  0.48393204]
V0:
[[ 3.38389131e-07 -1.87490029e-13 -4.65533610e-13 -7.73977856e-13
  -1.55022026e-15 -1.69092495e-13]
 [-1.87490029e-13  8.96044057e-10 -3.49001525e-15 -2.29899259e-15
  -6.38365350e-18 -8.33252836e-16]
 [-4.65533610e-13 -3.49001525e-15  3.26952668e-09 -4.20885469e-15
  -1.39855307e-17 -2.07642837e-15]
 [-7.73977856e-13 -2.29899259e-15 -4.20885469e-15  1.06091707e-07
  -1.27661520e-14 -1.87528240e-12]
 [-1.55022026e-15 -6.38365350e-18 -1.39855307e-17 -1.27661521e-14
   1.89408292e-10 -9.41476039e-15]
 [-1.69092495e-13 -8.33252836e-16 -2.07642837e-15 -1.87528240e-12
  -9.41476039e-15  4.11742998e-08]]
LogLike[0395]=-3069.243173
sigma_a=0.144882
R:
[[24.57056663 -1.39801034]
 [-1.39801034 23.56271286]]
m0:
[ 1.52483159 -0.1940014  -0.27101679 -1.08055208  0.35547294  0.48393204]
V0:
[[ 3.38388995e-07 -1.88032992e-13 -4.66976175e-13 -7.76067149e-13
  -1.55469291e-15 -1.69614165e-13]
 [-1.88032992e-13  8.96044054e-10 -3.50152377e-15 -2.30562547e-15
  -6.40330855e-18 -8.35987718e-16]
 [-4.66976175e-13 -3.50152377e-15  3.26952661e-09 -4.22183933e-15
  -1.40314343e-17 -2.08367061e-15]
 [-7.76067149e-13 -2.30562547e-15 -4.22183933e-15  1.06091693e-07
  -1.28031477e-14 -1.88109606e-12]
 [-1.55469291e-15 -6.40330855e-18 -1.40314343e-17 -1.28031477e-14
   1.89408292e-10 -9.44581385e-15]
 [-1.69614165e-13 -8.35987718e-16 -2.08367061e-15 -1.88109606e-12
  -9.44581385e-15  4.11742897e-08]]
LogLike[0396]=-3069.241318
sigma_a=0.144799
R:
[[24.57065395 -1.39798392]
 [-1.39798392 23.56279425]]
m0:
[ 1.52483158 -0.1940014  -0.27101679 -1.08055208  0.35547294  0.48393204]
V0:
[[ 3.38388859e-07 -1.88576107e-13 -4.68419352e-13 -7.78156639e-13
  -1.55916662e-15 -1.70136036e-13]
 [-1.88576107e-13  8.96044050e-10 -3.51303881e-15 -2.31225991e-15
  -6.42297104e-18 -8.38724037e-16]
 [-4.68419352e-13 -3.51303881e-15  3.26952655e-09 -4.23482894e-15
  -1.40773619e-17 -2.09091771e-15]
 [-7.78156639e-13 -2.31225991e-15 -4.23482894e-15  1.06091679e-07
  -1.28401537e-14 -1.88691219e-12]
 [-1.55916661e-15 -6.42297105e-18 -1.40773619e-17 -1.28401537e-14
   1.89408292e-10 -9.47688488e-15]
 [-1.70136036e-13 -8.38724037e-16 -2.09091771e-15 -1.88691219e-12
  -9.47688488e-15  4.11742796e-08]]
LogLike[0397]=-3069.239895
sigma_a=0.144735
R:
[[24.57076859 -1.39794941]
 [-1.39794941 23.5629013 ]]
m0:
[ 1.52483158 -0.1940014  -0.27101679 -1.08055208  0.35547294  0.48393204]
V0:
[[ 3.38388723e-07 -1.89119430e-13 -4.69863368e-13 -7.80246487e-13
  -1.56364194e-15 -1.70658200e-13]
 [-1.89119430e-13  8.96044047e-10 -3.52456275e-15 -2.31889676e-15
  -6.44264448e-18 -8.41462424e-16]
 [-4.69863368e-13 -3.52456275e-15  3.26952649e-09 -4.24782585e-15
  -1.41233243e-17 -2.09817171e-15]
 [-7.80246487e-13 -2.31889676e-15 -4.24782585e-15  1.06091665e-07
  -1.28771739e-14 -1.89273170e-12]
 [-1.56364194e-15 -6.44264449e-18 -1.41233243e-17 -1.28771739e-14
   1.89408292e-10 -9.50797991e-15]
 [-1.70658200e-13 -8.41462424e-16 -2.09817171e-15 -1.89273170e-12
  -9.50797991e-15  4.11742695e-08]]
LogLike[0398]=-3069.238733
sigma_a=0.144683
R:
[[24.57085815 -1.39792236]
 [-1.39792236 23.56298506]]
m0:
[ 1.52483157 -0.1940014  -0.27101679 -1.08055209  0.35547294  0.48393205]
V0:
[[ 3.38388586e-07 -1.89662913e-13 -4.71308029e-13 -7.82336582e-13
  -1.56811845e-15 -1.71180583e-13]
 [-1.89662913e-13  8.96044044e-10 -3.53609353e-15 -2.32553537e-15
  -6.46232610e-18 -8.44202368e-16]
 [-4.71308029e-13 -3.53609353e-15  3.26952642e-09 -4.26082822e-15
  -1.41693128e-17 -2.10543096e-15]
 [-7.82336582e-13 -2.32553537e-15 -4.26082822e-15  1.06091652e-07
  -1.29142050e-14 -1.89855381e-12]
 [-1.56811845e-15 -6.46232610e-18 -1.41693128e-17 -1.29142050e-14
   1.89408291e-10 -9.53909341e-15]
 [-1.71180583e-13 -8.44202368e-16 -2.10543096e-15 -1.89855381e-12
  -9.53909341e-15  4.11742594e-08]]
LogLike[0399]=-3069.236111
sigma_a=0.144565
R:
[[24.57093142 -1.39790022]
 [-1.39790022 23.56305369]]
m0:
[ 1.52483157 -0.1940014  -0.27101679 -1.08055209  0.35547294  0.48393205]
V0:
[[ 3.38388450e-07 -1.90206527e-13 -4.72753218e-13 -7.84426882e-13
  -1.57259594e-15 -1.71703146e-13]
 [-1.90206527e-13  8.96044041e-10 -3.54762992e-15 -2.33217542e-15
  -6.48201444e-18 -8.46943594e-16]
 [-4.72753218e-13 -3.54762992e-15  3.26952636e-09 -4.27383507e-15
  -1.42153228e-17 -2.11269450e-15]
 [-7.84426882e-13 -2.33217542e-15 -4.27383507e-15  1.06091638e-07
  -1.29512450e-14 -1.90437805e-12]
 [-1.57259594e-15 -6.48201444e-18 -1.42153228e-17 -1.29512451e-14
   1.89408291e-10 -9.57022206e-15]
 [-1.71703146e-13 -8.46943594e-16 -2.11269450e-15 -1.90437805e-12
  -9.57022206e-15  4.11742492e-08]]

Plots

Convergence

fig = go.Figure()
trace = go.Scatter(x=optim_res_ga["elapsed_time"], y=optim_res_ga["log_like"],
                  name="Gradient ascent", mode="lines+markers")
fig.add_trace(trace)
trace = go.Scatter(x=optim_res_em["elapsed_time"], y=optim_res_em["log_like"],
                   name="EM", mode="lines+markers")
fig.add_trace(trace)
fig.update_layout(xaxis_title="Elapsed Time (sec)",
                  yaxis_title="Log Likelihood")
fig

\(\sigma_a^2\) estimates

fig = go.Figure()
trace = go.Bar(x=["Gradient Ascent", "EM"],
               y=[optim_res_ga["estimates"]["sigma_a"].item()**2,
                  optim_res_em["estimates"]["sigma_a"]**2])
fig.add_trace(trace)
fig.add_hline(y=sigma_a_true**2)
fig.update_layout(xaxis_title="Estimation Method",
                  yaxis_title=r'$\sigma_a^2$')
fig

\(\sigma_x^2\) estimates

fig = go.Figure()
trace = go.Bar(x=["Gradient Ascent", "EM"],
               y=[optim_res_ga["estimates"]["sqrt_diag_R"][0].item()**2,
                  optim_res_em["estimates"]["R"][0, 0]])
fig.add_trace(trace)
fig.add_hline(y=sqrt_diag_R[0]**2)
fig.update_layout(xaxis_title="Estimation Method",
                  yaxis_title=r'$\sigma_x$')
fig

\(m_0[0]\) estimates

fig = go.Figure()
trace = go.Bar(x=["Gradient Ascent", "EM"],
               y=[optim_res_ga["estimates"]["m0"][0].item(),
                  optim_res_em["estimates"]["m0"][0]])
fig.add_trace(trace)
fig.add_hline(y=m0[0])
fig.update_layout(xaxis_title="Estimation Method",
                  yaxis_title=r'$m_0[0]$')
fig

\(V_0[0,0]\) estimates

fig = go.Figure()
trace = go.Bar(x=["Gradient Ascent", "EM"],
               y=[optim_res_ga["estimates"]["sqrt_diag_V0"][0].item()**2,
                  optim_res_em["estimates"]["V0"][0, 0]])
fig.add_trace(trace)
fig.add_hline(y=sqrt_diag_V0[0]**2)
fig.update_layout(xaxis_title="Estimation Method",
                  yaxis_title=r'$V_0[0, 0]$')
fig