Bayesian Sampler Examples

Examples of running each sampler avaiable in 3ML.

Before, that, let’s discuss setting up configuration default sampler with default parameters. We can set in our configuration a default algorithm and default setup parameters for the samplers. This can ease fitting when we are doing exploratory data analysis.

With any of the samplers, you can pass keywords to access their setups. Read each pacakges documentation for more details.

[1]:
from threeML import *
from threeML.plugins.XYLike import XYLike

import numpy as np
import dynesty
from jupyterthemes import jtplot

%matplotlib inline
jtplot.style(context="talk", fscale=1, ticks=True, grid=False)
silence_warnings()
set_threeML_style()
23:23:02 WARNING   The naima package is not available. Models that depend on it will not be         functions.py:48
                  available                                                                                        
         WARNING   The GSL library or the pygsl wrapper cannot be loaded. Models that depend on it  functions.py:69
                  will not be available.                                                                           
23:23:03 WARNING   The ebltable package is not available. Models that depend on it will not be     absorption.py:33
                  available                                                                                        
[2]:
threeML_config.bayesian.default_sampler
[2]:
<Sampler.emcee: 'emcee'>
[3]:
threeML_config.bayesian.emcee_setup
[3]:
{'n_burnin': None, 'n_iterations': 500, 'n_walkers': 50, 'seed': 5123}

If you simply run bayes_analysis.sample() the default sampler and its default parameters will be used.

Let’s make some data to fit.

[4]:
sin = Sin(K=1, f=0.1)
sin.phi.fix = True
sin.K.prior = Log_uniform_prior(lower_bound=0.5, upper_bound=1.5)
sin.f.prior = Uniform_prior(lower_bound=0, upper_bound=0.5)

model = Model(PointSource("demo", 0, 0, spectral_shape=sin))

x = np.linspace(-2 * np.pi, 4 * np.pi, 20)
yerr = np.random.uniform(0.01, 0.2, 20)


xyl = XYLike.from_function("demo", sin, x, yerr)
xyl.plot()

bayes_analysis = BayesianAnalysis(model, DataList(xyl))
23:23:05 INFO      Using Gaussian statistic (equivalent to chi^2) with the provided errors.            XYLike.py:93
23:23:06 INFO      Using Gaussian statistic (equivalent to chi^2) with the provided errors.            XYLike.py:93
../_images/notebooks_sampler_docs_5_2.png

emcee

[5]:
bayes_analysis.set_sampler("emcee")
bayes_analysis.sampler.setup(n_walkers=20, n_iterations=500)
bayes_analysis.sample()

xyl.plot()
bayes_analysis.results.corner_plot()
         INFO      sampler set to emcee                                                    bayesian_analysis.py:202
23:23:10 INFO      Mean acceptance fraction: 0.7108                                            emcee_sampler.py:157
         INFO      fit restored to maximum of posterior                                         sampler_base.py:178
         INFO      fit restored to maximum of posterior                                         sampler_base.py:178
Maximum a posteriori probability (MAP) point:

result unit
parameter
demo.spectrum.main.Sin.K (9.90 -0.19 +0.18) x 10^-1 1 / (cm2 keV s)
demo.spectrum.main.Sin.f (1.000 -0.005 +0.006) x 10^-1 rad / keV
Values of -log(posterior) at the minimum:

-log(posterior)
demo -7.226146
total -7.226146
Values of statistical measures:

statistical measures
AIC 19.158174
BIC 20.443756
DIC 18.507919
PDIC 2.027203
[5]:
../_images/notebooks_sampler_docs_7_12.png
../_images/notebooks_sampler_docs_7_13.png
../_images/notebooks_sampler_docs_7_14.png

multinest

[6]:
bayes_analysis.set_sampler("multinest")
bayes_analysis.sampler.setup(n_live_points=400, resume=False, auto_clean=True)
bayes_analysis.sample()

xyl.plot()
bayes_analysis.results.corner_plot()
23:23:11 INFO      sampler set to multinest                                                bayesian_analysis.py:202
 *****************************************************
 MultiNest v3.10
 Copyright Farhan Feroz & Mike Hobson
 Release Jul 2015

 no. of live points =  400
 dimensionality =    2
 *****************************************************
  analysing data from chains/fit-.txt ln(ev)=  -16.211884688691338      +/-  0.14135676411625850
 Total Likelihood Evaluations:         5367
 Sampling finished. Exiting MultiNest

23:23:12 INFO      fit restored to maximum of posterior                                         sampler_base.py:178
         INFO      fit restored to maximum of posterior                                         sampler_base.py:178
Maximum a posteriori probability (MAP) point:

result unit
parameter
demo.spectrum.main.Sin.K (9.89 -0.17 +0.20) x 10^-1 1 / (cm2 keV s)
demo.spectrum.main.Sin.f (1.001 +/- 0.006) x 10^-1 rad / keV
Values of -log(posterior) at the minimum:

-log(posterior)
demo -7.228148
total -7.228148
Values of statistical measures:

statistical measures
AIC 19.162179
BIC 20.447761
DIC 18.701802
PDIC 2.124429
log(Z) -7.040732
         INFO      deleting the chain directory chains                                     multinest_sampler.py:255
WARNING:root:Too few points to create valid contours
[6]:
../_images/notebooks_sampler_docs_9_13.png
../_images/notebooks_sampler_docs_9_14.png
../_images/notebooks_sampler_docs_9_15.png

dynesty

[7]:
bayes_analysis.set_sampler("dynesty_nested")
bayes_analysis.sampler.setup(n_live_points=400)
bayes_analysis.sample()

xyl.plot()
bayes_analysis.results.corner_plot()
23:23:13 INFO      sampler set to dynesty_nested                                           bayesian_analysis.py:202
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</pre>

3470it [00:04, 906.20it/s, bound: 6 | nc: 5 | ncall: 18427 | eff(%): 18.831 | loglstar: -inf < -9.156 < inf | logz: -18.497 +/- 0.144 | dlogz: 2.649 > 0.409]

end{sphinxVerbatim}

3470it [00:04, 906.20it/s, bound: 6 | nc: 5 | ncall: 18427 | eff(%): 18.831 | loglstar: -inf < -9.156 < inf | logz: -18.497 +/- 0.144 | dlogz: 2.649 > 0.409]

3580it [00:04, 818.12it/s, bound: 7 | nc: 1 | ncall: 18695 | eff(%): 19.150 | loglstar: -inf &lt; -8.655 &lt; inf | logz: -18.018 +/- 0.144 | dlogz: 1.975 &gt; 0.409]

</pre>

3580it [00:04, 818.12it/s, bound: 7 | nc: 1 | ncall: 18695 | eff(%): 19.150 | loglstar: -inf < -8.655 < inf | logz: -18.018 +/- 0.144 | dlogz: 1.975 > 0.409]

end{sphinxVerbatim}

3580it [00:04, 818.12it/s, bound: 7 | nc: 1 | ncall: 18695 | eff(%): 19.150 | loglstar: -inf < -8.655 < inf | logz: -18.018 +/- 0.144 | dlogz: 1.975 > 0.409]

3750it [00:04, 994.56it/s, bound: 7 | nc: 1 | ncall: 18938 | eff(%): 19.801 | loglstar: -inf &lt; -8.119 &lt; inf | logz: -17.485 +/- 0.144 | dlogz: 1.233 &gt; 0.409]

</pre>

3750it [00:04, 994.56it/s, bound: 7 | nc: 1 | ncall: 18938 | eff(%): 19.801 | loglstar: -inf < -8.119 < inf | logz: -17.485 +/- 0.144 | dlogz: 1.233 > 0.409]

end{sphinxVerbatim}

3750it [00:04, 994.56it/s, bound: 7 | nc: 1 | ncall: 18938 | eff(%): 19.801 | loglstar: -inf < -8.119 < inf | logz: -17.485 +/- 0.144 | dlogz: 1.233 > 0.409]

3919it [00:04, 1148.88it/s, bound: 7 | nc: 2 | ncall: 19279 | eff(%): 20.328 | loglstar: -inf &lt; -7.825 &lt; inf | logz: -17.145 +/- 0.144 | dlogz: 0.758 &gt; 0.409]

</pre>

3919it [00:04, 1148.88it/s, bound: 7 | nc: 2 | ncall: 19279 | eff(%): 20.328 | loglstar: -inf < -7.825 < inf | logz: -17.145 +/- 0.144 | dlogz: 0.758 > 0.409]

end{sphinxVerbatim}

3919it [00:04, 1148.88it/s, bound: 7 | nc: 2 | ncall: 19279 | eff(%): 20.328 | loglstar: -inf < -7.825 < inf | logz: -17.145 +/- 0.144 | dlogz: 0.758 > 0.409]

4051it [00:04, 946.65it/s, bound: 8 | nc: 2 | ncall: 19440 | eff(%): 20.838 | loglstar: -inf &lt; -7.654 &lt; inf | logz: -16.968 +/- 0.144 | dlogz: 0.521 &gt; 0.409]

</pre>

4051it [00:04, 946.65it/s, bound: 8 | nc: 2 | ncall: 19440 | eff(%): 20.838 | loglstar: -inf < -7.654 < inf | logz: -16.968 +/- 0.144 | dlogz: 0.521 > 0.409]

end{sphinxVerbatim}

4051it [00:04, 946.65it/s, bound: 8 | nc: 2 | ncall: 19440 | eff(%): 20.838 | loglstar: -inf < -7.654 < inf | logz: -16.968 +/- 0.144 | dlogz: 0.521 > 0.409]

4137it [00:05, 820.01it/s, +400 | bound: 8 | nc: 1 | ncall: 19965 | eff(%): 23.189 | loglstar: -inf &lt; -7.237 &lt; inf | logz: -16.531 +/- 0.144 | dlogz: 0.001 &gt; 0.409]

</pre>

4137it [00:05, 820.01it/s, +400 | bound: 8 | nc: 1 | ncall: 19965 | eff(%): 23.189 | loglstar: -inf < -7.237 < inf | logz: -16.531 +/- 0.144 | dlogz: 0.001 > 0.409]

end{sphinxVerbatim}

4137it [00:05, 820.01it/s, +400 | bound: 8 | nc: 1 | ncall: 19965 | eff(%): 23.189 | loglstar: -inf < -7.237 < inf | logz: -16.531 +/- 0.144 | dlogz: 0.001 > 0.409]


23:23:18 INFO      fit restored to maximum of posterior                                         sampler_base.py:178
         INFO      fit restored to maximum of posterior                                         sampler_base.py:178
Maximum a posteriori probability (MAP) point:

result unit
parameter
demo.spectrum.main.Sin.K (9.90 -0.17 +0.18) x 10^-1 1 / (cm2 keV s)
demo.spectrum.main.Sin.f (1.000 -0.005 +0.006) x 10^-1 rad / keV
Values of -log(posterior) at the minimum:

-log(posterior)
demo -7.227056
total -7.227056
Values of statistical measures:

statistical measures
AIC 19.159994
BIC 20.445576
DIC 18.309470
PDIC 1.928298
log(Z) -7.179301
[7]:
../_images/notebooks_sampler_docs_11_41.png
../_images/notebooks_sampler_docs_11_42.png
../_images/notebooks_sampler_docs_11_43.png
[8]:
bayes_analysis.set_sampler("dynesty_dynamic")
bayes_analysis.sampler.setup(
    stop_function=dynesty.utils.old_stopping_function, n_effective=None
)
bayes_analysis.sample()

xyl.plot()
bayes_analysis.results.corner_plot()
23:23:19 INFO      sampler set to dynesty_dynamic                                          bayesian_analysis.py:202
0it [00:00, ?it/s]

</pre>

0it [00:00, ?it/s]

end{sphinxVerbatim}

0it [00:00, ?it/s]

88it [00:00, 879.87it/s, batch: 0 | bound: 0 | nc: 1 | ncall: 92 | eff(%): 14.865 | loglstar: -inf &lt; -4007.534 &lt; inf | logz: -4014.606 +/- 0.118 | dlogz: 3967.704 &gt; 0.010]

</pre>

88it [00:00, 879.87it/s, batch: 0 | bound: 0 | nc: 1 | ncall: 92 | eff(%): 14.865 | loglstar: -inf < -4007.534 < inf | logz: -4014.606 +/- 0.118 | dlogz: 3967.704 > 0.010]

end{sphinxVerbatim}

88it [00:00, 879.87it/s, batch: 0 | bound: 0 | nc: 1 | ncall: 92 | eff(%): 14.865 | loglstar: -inf < -4007.534 < inf | logz: -4014.606 +/- 0.118 | dlogz: 3967.704 > 0.010]

267it [00:00, 1414.52it/s, batch: 0 | bound: 0 | nc: 1 | ncall: 343 | eff(%): 31.673 | loglstar: -inf &lt; -2662.405 &lt; inf | logz: -2669.846 +/- 0.122 | dlogz: 2664.776 &gt; 0.010]

</pre>

267it [00:00, 1414.52it/s, batch: 0 | bound: 0 | nc: 1 | ncall: 343 | eff(%): 31.673 | loglstar: -inf < -2662.405 < inf | logz: -2669.846 +/- 0.122 | dlogz: 2664.776 > 0.010]

end{sphinxVerbatim}

267it [00:00, 1414.52it/s, batch: 0 | bound: 0 | nc: 1 | ncall: 343 | eff(%): 31.673 | loglstar: -inf < -2662.405 < inf | logz: -2669.846 +/- 0.122 | dlogz: 2664.776 > 0.010]

474it [00:00, 1712.38it/s, batch: 0 | bound: 0 | nc: 1 | ncall: 755 | eff(%): 37.769 | loglstar: -inf &lt; -2085.793 &lt; inf | logz: -2093.010 +/- 0.112 | dlogz: 2081.320 &gt; 0.010]

</pre>

474it [00:00, 1712.38it/s, batch: 0 | bound: 0 | nc: 1 | ncall: 755 | eff(%): 37.769 | loglstar: -inf < -2085.793 < inf | logz: -2093.010 +/- 0.112 | dlogz: 2081.320 > 0.010]

end{sphinxVerbatim}

474it [00:00, 1712.38it/s, batch: 0 | bound: 0 | nc: 1 | ncall: 755 | eff(%): 37.769 | loglstar: -inf < -2085.793 < inf | logz: -2093.010 +/- 0.112 | dlogz: 2081.320 > 0.010]

646it [00:00, 1551.91it/s, batch: 0 | bound: 0 | nc: 5 | ncall: 1290 | eff(%): 36.089 | loglstar: -inf &lt; -1749.221 &lt; inf | logz: -1756.681 +/- 0.117 | dlogz: 1744.874 &gt; 0.010]

</pre>

646it [00:00, 1551.91it/s, batch: 0 | bound: 0 | nc: 5 | ncall: 1290 | eff(%): 36.089 | loglstar: -inf < -1749.221 < inf | logz: -1756.681 +/- 0.117 | dlogz: 1744.874 > 0.010]

end{sphinxVerbatim}

646it [00:00, 1551.91it/s, batch: 0 | bound: 0 | nc: 5 | ncall: 1290 | eff(%): 36.089 | loglstar: -inf < -1749.221 < inf | logz: -1756.681 +/- 0.117 | dlogz: 1744.874 > 0.010]

804it [00:00, 1238.32it/s, batch: 0 | bound: 0 | nc: 8 | ncall: 2008 | eff(%): 32.057 | loglstar: -inf &lt; -1492.953 &lt; inf | logz: -1499.834 +/- 0.116 | dlogz: 1490.963 &gt; 0.010]

</pre>

804it [00:00, 1238.32it/s, batch: 0 | bound: 0 | nc: 8 | ncall: 2008 | eff(%): 32.057 | loglstar: -inf < -1492.953 < inf | logz: -1499.834 +/- 0.116 | dlogz: 1490.963 > 0.010]

end{sphinxVerbatim}

804it [00:00, 1238.32it/s, batch: 0 | bound: 0 | nc: 8 | ncall: 2008 | eff(%): 32.057 | loglstar: -inf < -1492.953 < inf | logz: -1499.834 +/- 0.116 | dlogz: 1490.963 > 0.010]

937it [00:00, 1199.83it/s, batch: 0 | bound: 0 | nc: 12 | ncall: 2663 | eff(%): 29.624 | loglstar: -inf &lt; -1333.926 &lt; inf | logz: -1341.949 +/- 0.119 | dlogz: 1333.326 &gt; 0.010]

</pre>

937it [00:00, 1199.83it/s, batch: 0 | bound: 0 | nc: 12 | ncall: 2663 | eff(%): 29.624 | loglstar: -inf < -1333.926 < inf | logz: -1341.949 +/- 0.119 | dlogz: 1333.326 > 0.010]

end{sphinxVerbatim}

937it [00:00, 1199.83it/s, batch: 0 | bound: 0 | nc: 12 | ncall: 2663 | eff(%): 29.624 | loglstar: -inf < -1333.926 < inf | logz: -1341.949 +/- 0.119 | dlogz: 1333.326 > 0.010]

1063it [00:00, 1003.51it/s, batch: 0 | bound: 0 | nc: 14 | ncall: 3554 | eff(%): 26.221 | loglstar: -inf &lt; -1255.914 &lt; inf | logz: -1264.048 +/- 0.115 | dlogz: 1254.852 &gt; 0.010]

</pre>

1063it [00:00, 1003.51it/s, batch: 0 | bound: 0 | nc: 14 | ncall: 3554 | eff(%): 26.221 | loglstar: -inf < -1255.914 < inf | logz: -1264.048 +/- 0.115 | dlogz: 1254.852 > 0.010]

end{sphinxVerbatim}

1063it [00:00, 1003.51it/s, batch: 0 | bound: 0 | nc: 14 | ncall: 3554 | eff(%): 26.221 | loglstar: -inf < -1255.914 < inf | logz: -1264.048 +/- 0.115 | dlogz: 1254.852 > 0.010]

1171it [00:01, 869.86it/s, batch: 0 | bound: 0 | nc: 26 | ncall: 4551 | eff(%): 23.184 | loglstar: -inf &lt; -1156.156 &lt; inf | logz: -1164.979 +/- 0.126 | dlogz: 1156.331 &gt; 0.010]

</pre>

1171it [00:01, 869.86it/s, batch: 0 | bound: 0 | nc: 26 | ncall: 4551 | eff(%): 23.184 | loglstar: -inf < -1156.156 < inf | logz: -1164.979 +/- 0.126 | dlogz: 1156.331 > 0.010]

end{sphinxVerbatim}

1171it [00:01, 869.86it/s, batch: 0 | bound: 0 | nc: 26 | ncall: 4551 | eff(%): 23.184 | loglstar: -inf < -1156.156 < inf | logz: -1164.979 +/- 0.126 | dlogz: 1156.331 > 0.010]

1265it [00:01, 760.43it/s, batch: 0 | bound: 0 | nc: 20 | ncall: 5496 | eff(%): 21.097 | loglstar: -inf &lt; -1062.596 &lt; inf | logz: -1070.414 +/- 0.121 | dlogz: 1060.613 &gt; 0.010]

</pre>

1265it [00:01, 760.43it/s, batch: 0 | bound: 0 | nc: 20 | ncall: 5496 | eff(%): 21.097 | loglstar: -inf < -1062.596 < inf | logz: -1070.414 +/- 0.121 | dlogz: 1060.613 > 0.010]

end{sphinxVerbatim}

1265it [00:01, 760.43it/s, batch: 0 | bound: 0 | nc: 20 | ncall: 5496 | eff(%): 21.097 | loglstar: -inf < -1062.596 < inf | logz: -1070.414 +/- 0.121 | dlogz: 1060.613 > 0.010]

1347it [00:01, 662.72it/s, batch: 0 | bound: 0 | nc: 5 | ncall: 6388 | eff(%): 19.556 | loglstar: -inf &lt; -837.799 &lt; inf | logz: -846.335 +/- 0.130 | dlogz: 836.987 &gt; 0.010]

</pre>

1347it [00:01, 662.72it/s, batch: 0 | bound: 0 | nc: 5 | ncall: 6388 | eff(%): 19.556 | loglstar: -inf < -837.799 < inf | logz: -846.335 +/- 0.130 | dlogz: 836.987 > 0.010]

end{sphinxVerbatim}

1347it [00:01, 662.72it/s, batch: 0 | bound: 0 | nc: 5 | ncall: 6388 | eff(%): 19.556 | loglstar: -inf < -837.799 < inf | logz: -846.335 +/- 0.130 | dlogz: 836.987 > 0.010]

1418it [00:01, 558.01it/s, batch: 0 | bound: 0 | nc: 60 | ncall: 7623 | eff(%): 17.457 | loglstar: -inf &lt; -667.019 &lt; inf | logz: -676.634 +/- 0.136 | dlogz: 668.725 &gt; 0.010]

</pre>

1418it [00:01, 558.01it/s, batch: 0 | bound: 0 | nc: 60 | ncall: 7623 | eff(%): 17.457 | loglstar: -inf < -667.019 < inf | logz: -676.634 +/- 0.136 | dlogz: 668.725 > 0.010]

end{sphinxVerbatim}

1418it [00:01, 558.01it/s, batch: 0 | bound: 0 | nc: 60 | ncall: 7623 | eff(%): 17.457 | loglstar: -inf < -667.019 < inf | logz: -676.634 +/- 0.136 | dlogz: 668.725 > 0.010]

1478it [00:01, 436.04it/s, batch: 0 | bound: 0 | nc: 22 | ncall: 8796 | eff(%): 15.899 | loglstar: -inf &lt; -568.123 &lt; inf | logz: -577.313 +/- 0.131 | dlogz: 567.861 &gt; 0.010]

</pre>

1478it [00:01, 436.04it/s, batch: 0 | bound: 0 | nc: 22 | ncall: 8796 | eff(%): 15.899 | loglstar: -inf < -568.123 < inf | logz: -577.313 +/- 0.131 | dlogz: 567.861 > 0.010]

end{sphinxVerbatim}

1478it [00:01, 436.04it/s, batch: 0 | bound: 0 | nc: 22 | ncall: 8796 | eff(%): 15.899 | loglstar: -inf < -568.123 < inf | logz: -577.313 +/- 0.131 | dlogz: 567.861 > 0.010]

1528it [00:02, 382.07it/s, batch: 0 | bound: 0 | nc: 4 | ncall: 9774 | eff(%): 14.872 | loglstar: -inf &lt; -496.094 &lt; inf | logz: -505.290 +/- 0.133 | dlogz: 495.770 &gt; 0.010]

</pre>

1528it [00:02, 382.07it/s, batch: 0 | bound: 0 | nc: 4 | ncall: 9774 | eff(%): 14.872 | loglstar: -inf < -496.094 < inf | logz: -505.290 +/- 0.133 | dlogz: 495.770 > 0.010]

end{sphinxVerbatim}

1528it [00:02, 382.07it/s, batch: 0 | bound: 0 | nc: 4 | ncall: 9774 | eff(%): 14.872 | loglstar: -inf < -496.094 < inf | logz: -505.290 +/- 0.133 | dlogz: 495.770 > 0.010]

1570it [00:02, 343.41it/s, batch: 0 | bound: 0 | nc: 11 | ncall: 10584 | eff(%): 14.165 | loglstar: -inf &lt; -438.334 &lt; inf | logz: -447.191 +/- 0.129 | dlogz: 437.051 &gt; 0.010]

</pre>

1570it [00:02, 343.41it/s, batch: 0 | bound: 0 | nc: 11 | ncall: 10584 | eff(%): 14.165 | loglstar: -inf < -438.334 < inf | logz: -447.191 +/- 0.129 | dlogz: 437.051 > 0.010]

end{sphinxVerbatim}

1570it [00:02, 343.41it/s, batch: 0 | bound: 0 | nc: 11 | ncall: 10584 | eff(%): 14.165 | loglstar: -inf < -438.334 < inf | logz: -447.191 +/- 0.129 | dlogz: 437.051 > 0.010]

1607it [00:02, 317.81it/s, batch: 0 | bound: 0 | nc: 10 | ncall: 11462 | eff(%): 13.434 | loglstar: -inf &lt; -396.455 &lt; inf | logz: -405.809 +/- 0.130 | dlogz: 395.720 &gt; 0.010]

</pre>

1607it [00:02, 317.81it/s, batch: 0 | bound: 0 | nc: 10 | ncall: 11462 | eff(%): 13.434 | loglstar: -inf < -396.455 < inf | logz: -405.809 +/- 0.130 | dlogz: 395.720 > 0.010]

end{sphinxVerbatim}

1607it [00:02, 317.81it/s, batch: 0 | bound: 0 | nc: 10 | ncall: 11462 | eff(%): 13.434 | loglstar: -inf < -396.455 < inf | logz: -405.809 +/- 0.130 | dlogz: 395.720 > 0.010]

1640it [00:02, 293.04it/s, batch: 0 | bound: 0 | nc: 20 | ncall: 12490 | eff(%): 12.625 | loglstar: -inf &lt; -378.069 &lt; inf | logz: -387.346 +/- 0.128 | dlogz: 377.156 &gt; 0.010]

</pre>

1640it [00:02, 293.04it/s, batch: 0 | bound: 0 | nc: 20 | ncall: 12490 | eff(%): 12.625 | loglstar: -inf < -378.069 < inf | logz: -387.346 +/- 0.128 | dlogz: 377.156 > 0.010]

end{sphinxVerbatim}

1640it [00:02, 293.04it/s, batch: 0 | bound: 0 | nc: 20 | ncall: 12490 | eff(%): 12.625 | loglstar: -inf < -378.069 < inf | logz: -387.346 +/- 0.128 | dlogz: 377.156 > 0.010]

1672it [00:02, 295.26it/s, batch: 0 | bound: 0 | nc: 46 | ncall: 13152 | eff(%): 12.247 | loglstar: -inf &lt; -354.229 &lt; inf | logz: -363.090 +/- 0.126 | dlogz: 352.660 &gt; 0.010]

</pre>

1672it [00:02, 295.26it/s, batch: 0 | bound: 0 | nc: 46 | ncall: 13152 | eff(%): 12.247 | loglstar: -inf < -354.229 < inf | logz: -363.090 +/- 0.126 | dlogz: 352.660 > 0.010]

end{sphinxVerbatim}

1672it [00:02, 295.26it/s, batch: 0 | bound: 0 | nc: 46 | ncall: 13152 | eff(%): 12.247 | loglstar: -inf < -354.229 < inf | logz: -363.090 +/- 0.126 | dlogz: 352.660 > 0.010]

1703it [00:02, 294.18it/s, batch: 0 | bound: 0 | nc: 48 | ncall: 13834 | eff(%): 11.881 | loglstar: -inf &lt; -331.778 &lt; inf | logz: -340.991 +/- 0.129 | dlogz: 330.709 &gt; 0.010]

</pre>

1703it [00:02, 294.18it/s, batch: 0 | bound: 0 | nc: 48 | ncall: 13834 | eff(%): 11.881 | loglstar: -inf < -331.778 < inf | logz: -340.991 +/- 0.129 | dlogz: 330.709 > 0.010]

end{sphinxVerbatim}

1703it [00:02, 294.18it/s, batch: 0 | bound: 0 | nc: 48 | ncall: 13834 | eff(%): 11.881 | loglstar: -inf < -331.778 < inf | logz: -340.991 +/- 0.129 | dlogz: 330.709 > 0.010]

1733it [00:02, 270.74it/s, batch: 0 | bound: 0 | nc: 69 | ncall: 14741 | eff(%): 11.371 | loglstar: -inf &lt; -312.097 &lt; inf | logz: -320.676 +/- 0.125 | dlogz: 309.967 &gt; 0.010]

</pre>

1733it [00:02, 270.74it/s, batch: 0 | bound: 0 | nc: 69 | ncall: 14741 | eff(%): 11.371 | loglstar: -inf < -312.097 < inf | logz: -320.676 +/- 0.125 | dlogz: 309.967 > 0.010]

end{sphinxVerbatim}

1733it [00:02, 270.74it/s, batch: 0 | bound: 0 | nc: 69 | ncall: 14741 | eff(%): 11.371 | loglstar: -inf < -312.097 < inf | logz: -320.676 +/- 0.125 | dlogz: 309.967 > 0.010]

1761it [00:02, 265.69it/s, batch: 0 | bound: 0 | nc: 60 | ncall: 15320 | eff(%): 11.131 | loglstar: -inf &lt; -297.736 &lt; inf | logz: -307.093 +/- 0.129 | dlogz: 296.703 &gt; 0.010]

</pre>

1761it [00:02, 265.69it/s, batch: 0 | bound: 0 | nc: 60 | ncall: 15320 | eff(%): 11.131 | loglstar: -inf < -297.736 < inf | logz: -307.093 +/- 0.129 | dlogz: 296.703 > 0.010]

end{sphinxVerbatim}

1761it [00:02, 265.69it/s, batch: 0 | bound: 0 | nc: 60 | ncall: 15320 | eff(%): 11.131 | loglstar: -inf < -297.736 < inf | logz: -307.093 +/- 0.129 | dlogz: 296.703 > 0.010]

1788it [00:03, 222.32it/s, batch: 0 | bound: 0 | nc: 25 | ncall: 16043 | eff(%): 10.808 | loglstar: -inf &lt; -283.204 &lt; inf | logz: -292.501 +/- 0.131 | dlogz: 282.171 &gt; 0.010]

</pre>

1788it [00:03, 222.32it/s, batch: 0 | bound: 0 | nc: 25 | ncall: 16043 | eff(%): 10.808 | loglstar: -inf < -283.204 < inf | logz: -292.501 +/- 0.131 | dlogz: 282.171 > 0.010]

end{sphinxVerbatim}

1788it [00:03, 222.32it/s, batch: 0 | bound: 0 | nc: 25 | ncall: 16043 | eff(%): 10.808 | loglstar: -inf < -283.204 < inf | logz: -292.501 +/- 0.131 | dlogz: 282.171 > 0.010]

1812it [00:03, 176.29it/s, batch: 0 | bound: 0 | nc: 84 | ncall: 16815 | eff(%): 10.465 | loglstar: -inf &lt; -269.782 &lt; inf | logz: -278.803 +/- 0.130 | dlogz: 268.170 &gt; 0.010]

</pre>

1812it [00:03, 176.29it/s, batch: 0 | bound: 0 | nc: 84 | ncall: 16815 | eff(%): 10.465 | loglstar: -inf < -269.782 < inf | logz: -278.803 +/- 0.130 | dlogz: 268.170 > 0.010]

end{sphinxVerbatim}

1812it [00:03, 176.29it/s, batch: 0 | bound: 0 | nc: 84 | ncall: 16815 | eff(%): 10.465 | loglstar: -inf < -269.782 < inf | logz: -278.803 +/- 0.130 | dlogz: 268.170 > 0.010]

1832it [00:03, 156.12it/s, batch: 0 | bound: 0 | nc: 27 | ncall: 17398 | eff(%): 10.236 | loglstar: -inf &lt; -259.464 &lt; inf | logz: -268.523 +/- 0.128 | dlogz: 257.744 &gt; 0.010]

</pre>

1832it [00:03, 156.12it/s, batch: 0 | bound: 0 | nc: 27 | ncall: 17398 | eff(%): 10.236 | loglstar: -inf < -259.464 < inf | logz: -268.523 +/- 0.128 | dlogz: 257.744 > 0.010]

end{sphinxVerbatim}

1832it [00:03, 156.12it/s, batch: 0 | bound: 0 | nc: 27 | ncall: 17398 | eff(%): 10.236 | loglstar: -inf < -259.464 < inf | logz: -268.523 +/- 0.128 | dlogz: 257.744 > 0.010]

1849it [00:03, 99.61it/s, batch: 0 | bound: 0 | nc: 3 | ncall: 17927 | eff(%): 10.034 | loglstar: -inf &lt; -253.697 &lt; inf | logz: -262.449 +/- 0.125 | dlogz: 251.786 &gt; 0.010]

</pre>

1849it [00:03, 99.61it/s, batch: 0 | bound: 0 | nc: 3 | ncall: 17927 | eff(%): 10.034 | loglstar: -inf < -253.697 < inf | logz: -262.449 +/- 0.125 | dlogz: 251.786 > 0.010]

end{sphinxVerbatim}

1849it [00:03, 99.61it/s, batch: 0 | bound: 0 | nc: 3 | ncall: 17927 | eff(%): 10.034 | loglstar: -inf < -253.697 < inf | logz: -262.449 +/- 0.125 | dlogz: 251.786 > 0.010]

1863it [00:04, 53.91it/s, batch: 0 | bound: 1 | nc: 1 | ncall: 18060 | eff(%): 10.038 | loglstar: -inf &lt; -248.107 &lt; inf | logz: -256.938 +/- 0.128 | dlogz: 246.342 &gt; 0.010]

</pre>

1863it [00:04, 53.91it/s, batch: 0 | bound: 1 | nc: 1 | ncall: 18060 | eff(%): 10.038 | loglstar: -inf < -248.107 < inf | logz: -256.938 +/- 0.128 | dlogz: 246.342 > 0.010]

end{sphinxVerbatim}

1863it [00:04, 53.91it/s, batch: 0 | bound: 1 | nc: 1 | ncall: 18060 | eff(%): 10.038 | loglstar: -inf < -248.107 < inf | logz: -256.938 +/- 0.128 | dlogz: 246.342 > 0.010]

1873it [00:04, 55.70it/s, batch: 0 | bound: 1 | nc: 1 | ncall: 18073 | eff(%): 10.085 | loglstar: -inf &lt; -243.650 &lt; inf | logz: -252.767 +/- 0.129 | dlogz: 242.298 &gt; 0.010]

</pre>

1873it [00:04, 55.70it/s, batch: 0 | bound: 1 | nc: 1 | ncall: 18073 | eff(%): 10.085 | loglstar: -inf < -243.650 < inf | logz: -252.767 +/- 0.129 | dlogz: 242.298 > 0.010]

end{sphinxVerbatim}

1873it [00:04, 55.70it/s, batch: 0 | bound: 1 | nc: 1 | ncall: 18073 | eff(%): 10.085 | loglstar: -inf < -243.650 < inf | logz: -252.767 +/- 0.129 | dlogz: 242.298 > 0.010]

1985it [00:04, 182.55it/s, batch: 0 | bound: 1 | nc: 2 | ncall: 18244 | eff(%): 10.590 | loglstar: -inf &lt; -195.193 &lt; inf | logz: -204.726 +/- 0.132 | dlogz: 194.095 &gt; 0.010]

</pre>

1985it [00:04, 182.55it/s, batch: 0 | bound: 1 | nc: 2 | ncall: 18244 | eff(%): 10.590 | loglstar: -inf < -195.193 < inf | logz: -204.726 +/- 0.132 | dlogz: 194.095 > 0.010]

end{sphinxVerbatim}

1985it [00:04, 182.55it/s, batch: 0 | bound: 1 | nc: 2 | ncall: 18244 | eff(%): 10.590 | loglstar: -inf < -195.193 < inf | logz: -204.726 +/- 0.132 | dlogz: 194.095 > 0.010]

2087it [00:05, 303.96it/s, batch: 0 | bound: 1 | nc: 3 | ncall: 18422 | eff(%): 11.029 | loglstar: -inf &lt; -161.492 &lt; inf | logz: -170.605 +/- 0.129 | dlogz: 159.477 &gt; 0.010]

</pre>

2087it [00:05, 303.96it/s, batch: 0 | bound: 1 | nc: 3 | ncall: 18422 | eff(%): 11.029 | loglstar: -inf < -161.492 < inf | logz: -170.605 +/- 0.129 | dlogz: 159.477 > 0.010]

end{sphinxVerbatim}

2087it [00:05, 303.96it/s, batch: 0 | bound: 1 | nc: 3 | ncall: 18422 | eff(%): 11.029 | loglstar: -inf < -161.492 < inf | logz: -170.605 +/- 0.129 | dlogz: 159.477 > 0.010]

2146it [00:05, 338.02it/s, batch: 0 | bound: 1 | nc: 5 | ncall: 18541 | eff(%): 11.270 | loglstar: -inf &lt; -144.762 &lt; inf | logz: -153.624 +/- 0.126 | dlogz: 142.282 &gt; 0.010]

</pre>

2146it [00:05, 338.02it/s, batch: 0 | bound: 1 | nc: 5 | ncall: 18541 | eff(%): 11.270 | loglstar: -inf < -144.762 < inf | logz: -153.624 +/- 0.126 | dlogz: 142.282 > 0.010]

end{sphinxVerbatim}

2146it [00:05, 338.02it/s, batch: 0 | bound: 1 | nc: 5 | ncall: 18541 | eff(%): 11.270 | loglstar: -inf < -144.762 < inf | logz: -153.624 +/- 0.126 | dlogz: 142.282 > 0.010]

2238it [00:05, 448.65it/s, batch: 0 | bound: 1 | nc: 1 | ncall: 18766 | eff(%): 11.616 | loglstar: -inf &lt; -124.660 &lt; inf | logz: -133.729 +/- 0.128 | dlogz: 122.191 &gt; 0.010]

</pre>

2238it [00:05, 448.65it/s, batch: 0 | bound: 1 | nc: 1 | ncall: 18766 | eff(%): 11.616 | loglstar: -inf < -124.660 < inf | logz: -133.729 +/- 0.128 | dlogz: 122.191 > 0.010]

end{sphinxVerbatim}

2238it [00:05, 448.65it/s, batch: 0 | bound: 1 | nc: 1 | ncall: 18766 | eff(%): 11.616 | loglstar: -inf < -124.660 < inf | logz: -133.729 +/- 0.128 | dlogz: 122.191 > 0.010]

2304it [00:05, 269.05it/s, batch: 0 | bound: 2 | nc: 2 | ncall: 18866 | eff(%): 11.897 | loglstar: -inf &lt; -109.593 &lt; inf | logz: -118.638 +/- 0.128 | dlogz: 106.947 &gt; 0.010]

</pre>

2304it [00:05, 269.05it/s, batch: 0 | bound: 2 | nc: 2 | ncall: 18866 | eff(%): 11.897 | loglstar: -inf < -109.593 < inf | logz: -118.638 +/- 0.128 | dlogz: 106.947 > 0.010]

end{sphinxVerbatim}

2304it [00:05, 269.05it/s, batch: 0 | bound: 2 | nc: 2 | ncall: 18866 | eff(%): 11.897 | loglstar: -inf < -109.593 < inf | logz: -118.638 +/- 0.128 | dlogz: 106.947 > 0.010]

2500it [00:05, 510.04it/s, batch: 0 | bound: 2 | nc: 2 | ncall: 19167 | eff(%): 12.712 | loglstar: -inf &lt; -72.734 &lt; inf | logz: -82.302 +/- 0.131 | dlogz: 70.242 &gt; 0.010]

</pre>

2500it [00:05, 510.04it/s, batch: 0 | bound: 2 | nc: 2 | ncall: 19167 | eff(%): 12.712 | loglstar: -inf < -72.734 < inf | logz: -82.302 +/- 0.131 | dlogz: 70.242 > 0.010]

end{sphinxVerbatim}

2500it [00:05, 510.04it/s, batch: 0 | bound: 2 | nc: 2 | ncall: 19167 | eff(%): 12.712 | loglstar: -inf < -72.734 < inf | logz: -82.302 +/- 0.131 | dlogz: 70.242 > 0.010]

2663it [00:05, 697.43it/s, batch: 0 | bound: 2 | nc: 4 | ncall: 19539 | eff(%): 13.289 | loglstar: -inf &lt; -53.953 &lt; inf | logz: -63.142 +/- 0.128 | dlogz: 50.660 &gt; 0.010]

</pre>

2663it [00:05, 697.43it/s, batch: 0 | bound: 2 | nc: 4 | ncall: 19539 | eff(%): 13.289 | loglstar: -inf < -53.953 < inf | logz: -63.142 +/- 0.128 | dlogz: 50.660 > 0.010]

end{sphinxVerbatim}

2663it [00:05, 697.43it/s, batch: 0 | bound: 2 | nc: 4 | ncall: 19539 | eff(%): 13.289 | loglstar: -inf < -53.953 < inf | logz: -63.142 +/- 0.128 | dlogz: 50.660 > 0.010]

2777it [00:06, 540.36it/s, batch: 0 | bound: 3 | nc: 2 | ncall: 19676 | eff(%): 13.764 | loglstar: -inf &lt; -44.050 &lt; inf | logz: -53.369 +/- 0.127 | dlogz: 40.649 &gt; 0.010]

</pre>

2777it [00:06, 540.36it/s, batch: 0 | bound: 3 | nc: 2 | ncall: 19676 | eff(%): 13.764 | loglstar: -inf < -44.050 < inf | logz: -53.369 +/- 0.127 | dlogz: 40.649 > 0.010]

end{sphinxVerbatim}

2777it [00:06, 540.36it/s, batch: 0 | bound: 3 | nc: 2 | ncall: 19676 | eff(%): 13.764 | loglstar: -inf < -44.050 < inf | logz: -53.369 +/- 0.127 | dlogz: 40.649 > 0.010]

2905it [00:06, 659.06it/s, batch: 0 | bound: 3 | nc: 2 | ncall: 19885 | eff(%): 14.251 | loglstar: -inf &lt; -34.502 &lt; inf | logz: -43.826 +/- 0.129 | dlogz: 30.829 &gt; 0.010]

</pre>

2905it [00:06, 659.06it/s, batch: 0 | bound: 3 | nc: 2 | ncall: 19885 | eff(%): 14.251 | loglstar: -inf < -34.502 < inf | logz: -43.826 +/- 0.129 | dlogz: 30.829 > 0.010]

end{sphinxVerbatim}

2905it [00:06, 659.06it/s, batch: 0 | bound: 3 | nc: 2 | ncall: 19885 | eff(%): 14.251 | loglstar: -inf < -34.502 < inf | logz: -43.826 +/- 0.129 | dlogz: 30.829 > 0.010]

3033it [00:06, 774.22it/s, batch: 0 | bound: 3 | nc: 1 | ncall: 20171 | eff(%): 14.673 | loglstar: -inf &lt; -28.319 &lt; inf | logz: -37.490 +/- 0.129 | dlogz: 24.215 &gt; 0.010]

</pre>

3033it [00:06, 774.22it/s, batch: 0 | bound: 3 | nc: 1 | ncall: 20171 | eff(%): 14.673 | loglstar: -inf < -28.319 < inf | logz: -37.490 +/- 0.129 | dlogz: 24.215 > 0.010]

end{sphinxVerbatim}

3033it [00:06, 774.22it/s, batch: 0 | bound: 3 | nc: 1 | ncall: 20171 | eff(%): 14.673 | loglstar: -inf < -28.319 < inf | logz: -37.490 +/- 0.129 | dlogz: 24.215 > 0.010]

3143it [00:06, 528.10it/s, batch: 0 | bound: 4 | nc: 1 | ncall: 20358 | eff(%): 15.069 | loglstar: -inf &lt; -23.920 &lt; inf | logz: -33.005 +/- 0.128 | dlogz: 19.498 &gt; 0.010]

</pre>

3143it [00:06, 528.10it/s, batch: 0 | bound: 4 | nc: 1 | ncall: 20358 | eff(%): 15.069 | loglstar: -inf < -23.920 < inf | logz: -33.005 +/- 0.128 | dlogz: 19.498 > 0.010]

end{sphinxVerbatim}

3143it [00:06, 528.10it/s, batch: 0 | bound: 4 | nc: 1 | ncall: 20358 | eff(%): 15.069 | loglstar: -inf < -23.920 < inf | logz: -33.005 +/- 0.128 | dlogz: 19.498 > 0.010]

3362it [00:07, 774.37it/s, batch: 0 | bound: 4 | nc: 1 | ncall: 20690 | eff(%): 15.866 | loglstar: -inf &lt; -17.957 &lt; inf | logz: -26.850 +/- 0.127 | dlogz: 12.890 &gt; 0.010]

</pre>

3362it [00:07, 774.37it/s, batch: 0 | bound: 4 | nc: 1 | ncall: 20690 | eff(%): 15.866 | loglstar: -inf < -17.957 < inf | logz: -26.850 +/- 0.127 | dlogz: 12.890 > 0.010]

end{sphinxVerbatim}

3362it [00:07, 774.37it/s, batch: 0 | bound: 4 | nc: 1 | ncall: 20690 | eff(%): 15.866 | loglstar: -inf < -17.957 < inf | logz: -26.850 +/- 0.127 | dlogz: 12.890 > 0.010]

3520it [00:07, 753.29it/s, batch: 0 | bound: 5 | nc: 1 | ncall: 21054 | eff(%): 16.331 | loglstar: -inf &lt; -14.823 &lt; inf | logz: -23.901 +/- 0.128 | dlogz: 9.628 &gt; 0.010]

</pre>

3520it [00:07, 753.29it/s, batch: 0 | bound: 5 | nc: 1 | ncall: 21054 | eff(%): 16.331 | loglstar: -inf < -14.823 < inf | logz: -23.901 +/- 0.128 | dlogz: 9.628 > 0.010]

end{sphinxVerbatim}

3520it [00:07, 753.29it/s, batch: 0 | bound: 5 | nc: 1 | ncall: 21054 | eff(%): 16.331 | loglstar: -inf < -14.823 < inf | logz: -23.901 +/- 0.128 | dlogz: 9.628 > 0.010]

3771it [00:07, 1059.79it/s, batch: 0 | bound: 5 | nc: 2 | ncall: 21376 | eff(%): 17.238 | loglstar: -inf &lt; -11.739 &lt; inf | logz: -20.792 +/- 0.127 | dlogz: 6.031 &gt; 0.010]

</pre>

3771it [00:07, 1059.79it/s, batch: 0 | bound: 5 | nc: 2 | ncall: 21376 | eff(%): 17.238 | loglstar: -inf < -11.739 < inf | logz: -20.792 +/- 0.127 | dlogz: 6.031 > 0.010]

end{sphinxVerbatim}

3771it [00:07, 1059.79it/s, batch: 0 | bound: 5 | nc: 2 | ncall: 21376 | eff(%): 17.238 | loglstar: -inf < -11.739 < inf | logz: -20.792 +/- 0.127 | dlogz: 6.031 > 0.010]

3935it [00:07, 1174.37it/s, batch: 0 | bound: 5 | nc: 4 | ncall: 21719 | eff(%): 17.710 | loglstar: -inf &lt; -10.621 &lt; inf | logz: -19.547 +/- 0.127 | dlogz: 4.465 &gt; 0.010]

</pre>

3935it [00:07, 1174.37it/s, batch: 0 | bound: 5 | nc: 4 | ncall: 21719 | eff(%): 17.710 | loglstar: -inf < -10.621 < inf | logz: -19.547 +/- 0.127 | dlogz: 4.465 > 0.010]

end{sphinxVerbatim}

3935it [00:07, 1174.37it/s, batch: 0 | bound: 5 | nc: 4 | ncall: 21719 | eff(%): 17.710 | loglstar: -inf < -10.621 < inf | logz: -19.547 +/- 0.127 | dlogz: 4.465 > 0.010]

4088it [00:07, 989.22it/s, batch: 0 | bound: 6 | nc: 1 | ncall: 21962 | eff(%): 18.200 | loglstar: -inf &lt; -9.701 &lt; inf | logz: -18.733 +/- 0.127 | dlogz: 3.368 &gt; 0.010]

</pre>

4088it [00:07, 989.22it/s, batch: 0 | bound: 6 | nc: 1 | ncall: 21962 | eff(%): 18.200 | loglstar: -inf < -9.701 < inf | logz: -18.733 +/- 0.127 | dlogz: 3.368 > 0.010]

end{sphinxVerbatim}

4088it [00:07, 989.22it/s, batch: 0 | bound: 6 | nc: 1 | ncall: 21962 | eff(%): 18.200 | loglstar: -inf < -9.701 < inf | logz: -18.733 +/- 0.127 | dlogz: 3.368 > 0.010]

4240it [00:07, 1095.03it/s, batch: 0 | bound: 6 | nc: 2 | ncall: 22256 | eff(%): 18.632 | loglstar: -inf &lt; -9.097 &lt; inf | logz: -18.107 +/- 0.127 | dlogz: 2.488 &gt; 0.010]

</pre>

4240it [00:07, 1095.03it/s, batch: 0 | bound: 6 | nc: 2 | ncall: 22256 | eff(%): 18.632 | loglstar: -inf < -9.097 < inf | logz: -18.107 +/- 0.127 | dlogz: 2.488 > 0.010]

end{sphinxVerbatim}

4240it [00:07, 1095.03it/s, batch: 0 | bound: 6 | nc: 2 | ncall: 22256 | eff(%): 18.632 | loglstar: -inf < -9.097 < inf | logz: -18.107 +/- 0.127 | dlogz: 2.488 > 0.010]

4375it [00:08, 590.90it/s, batch: 0 | bound: 7 | nc: 1 | ncall: 22560 | eff(%): 18.972 | loglstar: -inf &lt; -8.681 &lt; inf | logz: -17.699 +/- 0.127 | dlogz: 1.888 &gt; 0.010]

</pre>

4375it [00:08, 590.90it/s, batch: 0 | bound: 7 | nc: 1 | ncall: 22560 | eff(%): 18.972 | loglstar: -inf < -8.681 < inf | logz: -17.699 +/- 0.127 | dlogz: 1.888 > 0.010]

end{sphinxVerbatim}

4375it [00:08, 590.90it/s, batch: 0 | bound: 7 | nc: 1 | ncall: 22560 | eff(%): 18.972 | loglstar: -inf < -8.681 < inf | logz: -17.699 +/- 0.127 | dlogz: 1.888 > 0.010]

4596it [00:08, 803.11it/s, batch: 0 | bound: 7 | nc: 1 | ncall: 22857 | eff(%): 19.677 | loglstar: -inf &lt; -8.187 &lt; inf | logz: -17.222 +/- 0.127 | dlogz: 1.176 &gt; 0.010]

</pre>

4596it [00:08, 803.11it/s, batch: 0 | bound: 7 | nc: 1 | ncall: 22857 | eff(%): 19.677 | loglstar: -inf < -8.187 < inf | logz: -17.222 +/- 0.127 | dlogz: 1.176 > 0.010]

end{sphinxVerbatim}

4596it [00:08, 803.11it/s, batch: 0 | bound: 7 | nc: 1 | ncall: 22857 | eff(%): 19.677 | loglstar: -inf < -8.187 < inf | logz: -17.222 +/- 0.127 | dlogz: 1.176 > 0.010]

4727it [00:08, 628.29it/s, batch: 0 | bound: 7 | nc: 1 | ncall: 23129 | eff(%): 20.005 | loglstar: -inf &lt; -7.949 &lt; inf | logz: -17.019 +/- 0.127 | dlogz: 0.878 &gt; 0.010]

</pre>

4727it [00:08, 628.29it/s, batch: 0 | bound: 7 | nc: 1 | ncall: 23129 | eff(%): 20.005 | loglstar: -inf < -7.949 < inf | logz: -17.019 +/- 0.127 | dlogz: 0.878 > 0.010]

end{sphinxVerbatim}

4727it [00:08, 628.29it/s, batch: 0 | bound: 7 | nc: 1 | ncall: 23129 | eff(%): 20.005 | loglstar: -inf < -7.949 < inf | logz: -17.019 +/- 0.127 | dlogz: 0.878 > 0.010]

4830it [00:08, 570.36it/s, batch: 0 | bound: 8 | nc: 1 | ncall: 23341 | eff(%): 20.259 | loglstar: -inf &lt; -7.810 &lt; inf | logz: -16.890 +/- 0.127 | dlogz: 0.697 &gt; 0.010]

</pre>

4830it [00:08, 570.36it/s, batch: 0 | bound: 8 | nc: 1 | ncall: 23341 | eff(%): 20.259 | loglstar: -inf < -7.810 < inf | logz: -16.890 +/- 0.127 | dlogz: 0.697 > 0.010]

end{sphinxVerbatim}

4830it [00:08, 570.36it/s, batch: 0 | bound: 8 | nc: 1 | ncall: 23341 | eff(%): 20.259 | loglstar: -inf < -7.810 < inf | logz: -16.890 +/- 0.127 | dlogz: 0.697 > 0.010]

4967it [00:09, 684.82it/s, batch: 0 | bound: 8 | nc: 2 | ncall: 23539 | eff(%): 20.662 | loglstar: -inf &lt; -7.669 &lt; inf | logz: -16.755 +/- 0.127 | dlogz: 0.512 &gt; 0.010]

</pre>

4967it [00:09, 684.82it/s, batch: 0 | bound: 8 | nc: 2 | ncall: 23539 | eff(%): 20.662 | loglstar: -inf < -7.669 < inf | logz: -16.755 +/- 0.127 | dlogz: 0.512 > 0.010]

end{sphinxVerbatim}

4967it [00:09, 684.82it/s, batch: 0 | bound: 8 | nc: 2 | ncall: 23539 | eff(%): 20.662 | loglstar: -inf < -7.669 < inf | logz: -16.755 +/- 0.127 | dlogz: 0.512 > 0.010]

5067it [00:09, 663.93it/s, batch: 0 | bound: 8 | nc: 1 | ncall: 23703 | eff(%): 20.935 | loglstar: -inf &lt; -7.602 &lt; inf | logz: -16.677 +/- 0.127 | dlogz: 0.410 &gt; 0.010]

</pre>

5067it [00:09, 663.93it/s, batch: 0 | bound: 8 | nc: 1 | ncall: 23703 | eff(%): 20.935 | loglstar: -inf < -7.602 < inf | logz: -16.677 +/- 0.127 | dlogz: 0.410 > 0.010]

end{sphinxVerbatim}

5067it [00:09, 663.93it/s, batch: 0 | bound: 8 | nc: 1 | ncall: 23703 | eff(%): 20.935 | loglstar: -inf < -7.602 < inf | logz: -16.677 +/- 0.127 | dlogz: 0.410 > 0.010]

5198it [00:09, 779.46it/s, batch: 0 | bound: 8 | nc: 5 | ncall: 23998 | eff(%): 21.218 | loglstar: -inf &lt; -7.498 &lt; inf | logz: -16.595 +/- 0.127 | dlogz: 0.307 &gt; 0.010]

</pre>

5198it [00:09, 779.46it/s, batch: 0 | bound: 8 | nc: 5 | ncall: 23998 | eff(%): 21.218 | loglstar: -inf < -7.498 < inf | logz: -16.595 +/- 0.127 | dlogz: 0.307 > 0.010]

end{sphinxVerbatim}

5198it [00:09, 779.46it/s, batch: 0 | bound: 8 | nc: 5 | ncall: 23998 | eff(%): 21.218 | loglstar: -inf < -7.498 < inf | logz: -16.595 +/- 0.127 | dlogz: 0.307 > 0.010]

5299it [00:09, 672.20it/s, batch: 0 | bound: 9 | nc: 1 | ncall: 24135 | eff(%): 21.510 | loglstar: -inf &lt; -7.445 &lt; inf | logz: -16.545 +/- 0.127 | dlogz: 0.246 &gt; 0.010]

</pre>

5299it [00:09, 672.20it/s, batch: 0 | bound: 9 | nc: 1 | ncall: 24135 | eff(%): 21.510 | loglstar: -inf < -7.445 < inf | logz: -16.545 +/- 0.127 | dlogz: 0.246 > 0.010]

end{sphinxVerbatim}

5299it [00:09, 672.20it/s, batch: 0 | bound: 9 | nc: 1 | ncall: 24135 | eff(%): 21.510 | loglstar: -inf < -7.445 < inf | logz: -16.545 +/- 0.127 | dlogz: 0.246 > 0.010]

5469it [00:09, 869.38it/s, batch: 0 | bound: 9 | nc: 4 | ncall: 24396 | eff(%): 21.967 | loglstar: -inf &lt; -7.383 &lt; inf | logz: -16.480 +/- 0.127 | dlogz: 0.171 &gt; 0.010]

</pre>

5469it [00:09, 869.38it/s, batch: 0 | bound: 9 | nc: 4 | ncall: 24396 | eff(%): 21.967 | loglstar: -inf < -7.383 < inf | logz: -16.480 +/- 0.127 | dlogz: 0.171 > 0.010]

end{sphinxVerbatim}

5469it [00:09, 869.38it/s, batch: 0 | bound: 9 | nc: 4 | ncall: 24396 | eff(%): 21.967 | loglstar: -inf < -7.383 < inf | logz: -16.480 +/- 0.127 | dlogz: 0.171 > 0.010]

5609it [00:09, 983.17it/s, batch: 0 | bound: 9 | nc: 1 | ncall: 24680 | eff(%): 22.276 | loglstar: -inf &lt; -7.350 &lt; inf | logz: -16.441 +/- 0.127 | dlogz: 0.127 &gt; 0.010]

</pre>

5609it [00:09, 983.17it/s, batch: 0 | bound: 9 | nc: 1 | ncall: 24680 | eff(%): 22.276 | loglstar: -inf < -7.350 < inf | logz: -16.441 +/- 0.127 | dlogz: 0.127 > 0.010]

end{sphinxVerbatim}

5609it [00:09, 983.17it/s, batch: 0 | bound: 9 | nc: 1 | ncall: 24680 | eff(%): 22.276 | loglstar: -inf < -7.350 < inf | logz: -16.441 +/- 0.127 | dlogz: 0.127 > 0.010]

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23:23:34 INFO      fit restored to maximum of posterior                                         sampler_base.py:178
         INFO      fit restored to maximum of posterior                                         sampler_base.py:178
Maximum a posteriori probability (MAP) point:

result unit
parameter
demo.spectrum.main.Sin.K (9.90 -0.19 +0.18) x 10^-1 1 / (cm2 keV s)
demo.spectrum.main.Sin.f (1.001 -0.006 +0.005) x 10^-1 rad / keV
Values of -log(posterior) at the minimum:

-log(posterior)
demo -7.226211
total -7.226211
Values of statistical measures:

statistical measures
AIC 19.158304
BIC 20.443887
DIC 18.479790
PDIC 2.013406
log(Z) -7.080860
[8]:
../_images/notebooks_sampler_docs_12_86.png
../_images/notebooks_sampler_docs_12_87.png
../_images/notebooks_sampler_docs_12_88.png

zeus

[9]:
bayes_analysis.set_sampler("zeus")
bayes_analysis.sampler.setup(n_walkers=20, n_iterations=500)
bayes_analysis.sample()

xyl.plot()
bayes_analysis.results.corner_plot()
23:23:35 INFO      sampler set to zeus                                                     bayesian_analysis.py:202
WARNING:root:The sampler class has been deprecated. Please use the new EnsembleSampler class.
The run method has been deprecated and it will be removed. Please use the new run_mcmc method.
Initialising ensemble of 20 walkers...
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23:23:48 INFO      fit restored to maximum of posterior                                         sampler_base.py:178
         INFO      fit restored to maximum of posterior                                         sampler_base.py:178
Summary
-------
Number of Generations: 625
Number of Parameters: 2
Number of Walkers: 20
Number of Tuning Generations: 21
Scale Factor: 1.022713
Mean Integrated Autocorrelation Time: 3.12
Effective Sample Size: 4011.25
Number of Log Probability Evaluations: 67088
Effective Samples per Log Probability Evaluation: 0.059791
None
Maximum a posteriori probability (MAP) point:

result unit
parameter
demo.spectrum.main.Sin.K (9.90 -0.17 +0.18) x 10^-1 1 / (cm2 keV s)
demo.spectrum.main.Sin.f (1.001 +/- 0.005) x 10^-1 rad / keV
Values of -log(posterior) at the minimum:

-log(posterior)
demo -7.226169
total -7.226169
Values of statistical measures:

statistical measures
AIC 19.158220
BIC 20.443803
DIC 18.301932
PDIC 1.924389
[9]:
../_images/notebooks_sampler_docs_14_127.png
../_images/notebooks_sampler_docs_14_128.png
../_images/notebooks_sampler_docs_14_129.png

ultranest

[10]:
bayes_analysis.set_sampler("ultranest")
bayes_analysis.sampler.setup(
    min_num_live_points=400, frac_remain=0.5, use_mlfriends=False
)
bayes_analysis.sample()

xyl.plot()
bayes_analysis.results.corner_plot()
23:23:50 INFO      sampler set to ultranest                                                bayesian_analysis.py:202
[ultranest] Sampling 400 live points from prior ...
Z=-inf(0.00%) | Like=-8001.62..-34.01 [-8001.6173..-2320.0793] | it/evals=0/401 eff=0.0000% N=400
Z=-4478.6(0.00%) | Like=-4467.05..-34.01 [-8001.6173..-2320.0793] | it/evals=40/441 eff=97.5610% N=400
Z=-3773.3(0.00%) | Like=-3748.44..-9.36 [-8001.6173..-2320.0793] | it/evals=80/485 eff=94.1176% N=400
Z=-3549.0(0.00%) | Like=-3509.87..-9.36 [-8001.6173..-2320.0793] | it/evals=90/497 eff=92.7835% N=400
Z=-3234.4(0.00%) | Like=-3227.74..-9.36 [-8001.6173..-2320.0793] | it/evals=120/528 eff=93.7500% N=400
Z=-2916.9(0.00%) | Like=-2907.60..-9.36 [-8001.6173..-2320.0793] | it/evals=160/582 eff=87.9121% N=400
Z=-2670.2(0.00%) | Like=-2661.51..-9.36 [-8001.6173..-2320.0793] | it/evals=200/642 eff=82.6446% N=400
Z=-2447.3(0.00%) | Like=-2440.22..-9.36 [-8001.6173..-2320.0793] | it/evals=240/717 eff=75.7098% N=400
Z=-2326.0(0.00%) | Like=-2317.74..-9.36 [-2319.7346..-1614.4028] | it/evals=270/782 eff=70.6806% N=400
Z=-2309.4(0.00%) | Like=-2299.66..-9.36 [-2319.7346..-1614.4028] | it/evals=280/802 eff=69.6517% N=400
Z=-2160.8(0.00%) | Like=-2152.93..-9.36 [-2319.7346..-1614.4028] | it/evals=320/876 eff=67.2269% N=400
Z=-2053.5(0.00%) | Like=-2045.62..-9.36 [-2319.7346..-1614.4028] | it/evals=360/982 eff=61.8557% N=400
Z=-1986.2(0.00%) | Like=-1971.76..-9.36 [-2319.7346..-1614.4028] | it/evals=387/1076 eff=57.2485% N=400
Z=-1953.8(0.00%) | Like=-1945.53..-9.36 [-2319.7346..-1614.4028] | it/evals=400/1110 eff=56.3380% N=400
Z=-1867.7(0.00%) | Like=-1860.54..-9.36 [-2319.7346..-1614.4028] | it/evals=440/1188 eff=55.8376% N=400
Z=-1850.3(0.00%) | Like=-1842.48..-9.36 [-2319.7346..-1614.4028] | it/evals=450/1225 eff=54.5455% N=400
Z=-1775.7(0.00%) | Like=-1764.04..-9.36 [-2319.7346..-1614.4028] | it/evals=480/1325 eff=51.8919% N=400
Z=-1710.0(0.00%) | Like=-1699.87..-9.36 [-2319.7346..-1614.4028] | it/evals=520/1461 eff=49.0104% N=400
Z=-1609.1(0.00%) | Like=-1600.52..-9.36 [-1614.3826..-1255.9587] | it/evals=555/1580 eff=47.0339% N=400
Z=-1595.6(0.00%) | Like=-1582.63..-9.36 [-1614.3826..-1255.9587] | it/evals=560/1600 eff=46.6667% N=400
Z=-1512.1(0.00%) | Like=-1502.90..-9.36 [-1614.3826..-1255.9587] | it/evals=600/1785 eff=43.3213% N=400
Z=-1456.2(0.00%) | Like=-1449.54..-9.36 [-1614.3826..-1255.9587] | it/evals=630/1905 eff=41.8605% N=400
Z=-1441.5(0.00%) | Like=-1433.99..-9.36 [-1614.3826..-1255.9587] | it/evals=640/1932 eff=41.7755% N=400
Z=-1391.6(0.00%) | Like=-1384.80..-9.36 [-1614.3826..-1255.9587] | it/evals=680/2101 eff=39.9765% N=400
Z=-1328.8(0.00%) | Like=-1319.42..-9.36 [-1614.3826..-1255.9587] | it/evals=720/2307 eff=37.7556% N=400
Z=-1299.5(0.00%) | Like=-1291.43..-9.36 [-1614.3826..-1255.9587] | it/evals=757/2512 eff=35.8428% N=400
Z=-1297.9(0.00%) | Like=-1291.18..-9.36 [-1614.3826..-1255.9587] | it/evals=760/2519 eff=35.8660% N=400
Z=-1293.4(0.00%) | Like=-1285.98..-9.36 [-1614.3826..-1255.9587] | it/evals=770/2574 eff=35.4186% N=400
Z=-1275.4(0.00%) | Like=-1268.24..-9.36 [-1614.3826..-1255.9587] | it/evals=793/2731 eff=34.0197% N=400
Z=-1271.0(0.00%) | Like=-1263.61..-9.36 [-1614.3826..-1255.9587] | it/evals=800/2776 eff=33.6700% N=400
Z=-1265.5(0.00%) | Like=-1257.98..-9.36 [-1614.3826..-1255.9587] | it/evals=810/2835 eff=33.2649% N=400
Z=-1252.0(0.00%) | Like=-1245.56..-9.36 [-1255.7447..-569.2776] | it/evals=840/2978 eff=32.5834% N=400
Z=-1209.1(0.00%) | Like=-1200.49..-9.36 [-1255.7447..-569.2776] | it/evals=880/3238 eff=31.0078% N=400
Z=-1134.7(0.00%) | Like=-1122.78..-9.36 [-1255.7447..-569.2776] | it/evals=920/3441 eff=30.2532% N=400
Z=-1078.9(0.00%) | Like=-1069.34..-9.36 [-1255.7447..-569.2776] | it/evals=960/3746 eff=28.6910% N=400
Z=-997.1(0.00%) | Like=-983.15..-9.36 [-1255.7447..-569.2776] | it/evals=990/3951 eff=27.8795% N=400
Z=-948.4(0.00%) | Like=-930.38..-9.36 [-1255.7447..-569.2776] | it/evals=1000/3961 eff=28.0820% N=400
Z=-776.7(0.00%) | Like=-762.41..-9.36 [-1255.7447..-569.2776] | it/evals=1040/4013 eff=28.7849% N=400
Z=-645.5(0.00%) | Like=-635.32..-9.36 [-1255.7447..-569.2776] | it/evals=1080/4077 eff=29.3718% N=400
Z=-530.1(0.00%) | Like=-519.72..-9.36 [-568.6238..-240.6271] | it/evals=1120/4124 eff=30.0752% N=400
Z=-446.8(0.00%) | Like=-437.26..-9.36 [-568.6238..-240.6271] | it/evals=1160/4202 eff=30.5103% N=400
Z=-430.7(0.00%) | Like=-421.36..-9.36 [-568.6238..-240.6271] | it/evals=1170/4218 eff=30.6443% N=400
Z=-379.0(0.00%) | Like=-369.88..-7.44 [-568.6238..-240.6271] | it/evals=1200/4254 eff=31.1365% N=400
Z=-345.7(0.00%) | Like=-336.84..-7.44 [-568.6238..-240.6271] | it/evals=1240/4318 eff=31.6488% N=400
Z=-332.0(0.00%) | Like=-322.96..-7.44 [-568.6238..-240.6271] | it/evals=1260/4344 eff=31.9473% N=400
Z=-317.7(0.00%) | Like=-307.59..-7.44 [-568.6238..-240.6271] | it/evals=1280/4369 eff=32.2499% N=400
Z=-293.6(0.00%) | Like=-283.94..-7.44 [-568.6238..-240.6271] | it/evals=1320/4420 eff=32.8358% N=400
Z=-270.0(0.00%) | Like=-261.38..-7.44 [-568.6238..-240.6271] | it/evals=1350/4466 eff=33.2022% N=400
Z=-264.9(0.00%) | Like=-255.72..-7.44 [-568.6238..-240.6271] | it/evals=1360/4477 eff=33.3579% N=400
Z=-243.8(0.00%) | Like=-234.81..-7.44 [-240.5491..-124.3283] | it/evals=1400/4539 eff=33.8246% N=400
Z=-224.0(0.00%) | Like=-215.39..-7.44 [-240.5491..-124.3283] | it/evals=1440/4599 eff=34.2939% N=400
Z=-211.1(0.00%) | Like=-202.24..-7.44 [-240.5491..-124.3283] | it/evals=1480/4648 eff=34.8399% N=400
Z=-194.8(0.00%) | Like=-184.89..-7.44 [-240.5491..-124.3283] | it/evals=1520/4700 eff=35.3488% N=400
Z=-189.4(0.00%) | Like=-180.72..-7.44 [-240.5491..-124.3283] | it/evals=1530/4716 eff=35.4495% N=400
Z=-174.7(0.00%) | Like=-164.86..-7.44 [-240.5491..-124.3283] | it/evals=1560/4753 eff=35.8374% N=400
Z=-157.2(0.00%) | Like=-148.63..-7.44 [-240.5491..-124.3283] | it/evals=1600/4825 eff=36.1582% N=400
Z=-148.9(0.00%) | Like=-139.88..-7.44 [-240.5491..-124.3283] | it/evals=1620/4851 eff=36.3963% N=400
Z=-143.9(0.00%) | Like=-135.26..-7.44 [-240.5491..-124.3283] | it/evals=1640/4878 eff=36.6235% N=400
Z=-132.6(0.00%) | Like=-124.00..-7.44 [-124.1941..-63.4891] | it/evals=1680/4930 eff=37.0861% N=400
Z=-124.9(0.00%) | Like=-116.27..-7.44 [-124.1941..-63.4891] | it/evals=1710/4973 eff=37.3934% N=400
Z=-122.9(0.00%) | Like=-114.26..-7.44 [-124.1941..-63.4891] | it/evals=1720/4986 eff=37.5055% N=400
Z=-110.3(0.00%) | Like=-101.24..-7.44 [-124.1941..-63.4891] | it/evals=1760/5045 eff=37.8902% N=400
Z=-100.6(0.00%) | Like=-91.63..-7.44 [-124.1941..-63.4891] | it/evals=1800/5102 eff=38.2816% N=400
Z=-92.1(0.00%) | Like=-83.36..-7.44 [-124.1941..-63.4891] | it/evals=1840/5154 eff=38.7042% N=400
Z=-84.1(0.00%) | Like=-75.69..-7.44 [-124.1941..-63.4891] | it/evals=1880/5219 eff=39.0122% N=400
Z=-83.2(0.00%) | Like=-74.87..-7.44 [-124.1941..-63.4891] | it/evals=1890/5231 eff=39.1223% N=400
Z=-77.9(0.00%) | Like=-68.71..-7.44 [-124.1941..-63.4891] | it/evals=1920/5264 eff=39.4737% N=400
Z=-72.1(0.00%) | Like=-63.44..-7.44 [-63.4386..-34.4452] | it/evals=1960/5319 eff=39.8455% N=400
Z=-70.1(0.00%) | Like=-61.45..-7.44 [-63.4386..-34.4452] | it/evals=1980/5344 eff=40.0485% N=400
Z=-67.1(0.00%) | Like=-57.60..-7.44 [-63.4386..-34.4452] | it/evals=2000/5370 eff=40.2414% N=400
Z=-62.0(0.00%) | Like=-52.73..-7.44 [-63.4386..-34.4452] | it/evals=2033/5416 eff=40.5303% N=400
Z=-61.2(0.00%) | Like=-52.51..-7.44 [-63.4386..-34.4452] | it/evals=2040/5427 eff=40.5809% N=400
Z=-58.2(0.00%) | Like=-49.38..-7.44 [-63.4386..-34.4452] | it/evals=2070/5466 eff=40.8606% N=400
Z=-57.3(0.00%) | Like=-48.32..-7.44 [-63.4386..-34.4452] | it/evals=2080/5477 eff=40.9691% N=400
Z=-52.7(0.00%) | Like=-43.82..-7.37 [-63.4386..-34.4452] | it/evals=2120/5528 eff=41.3417% N=400
Z=-48.6(0.00%) | Like=-39.34..-7.29 [-63.4386..-34.4452] | it/evals=2160/5589 eff=41.6265% N=400
Z=-45.4(0.00%) | Like=-36.84..-7.29 [-63.4386..-34.4452] | it/evals=2200/5642 eff=41.9687% N=400
Z=-43.3(0.00%) | Like=-34.49..-7.29 [-63.4386..-34.4452] | it/evals=2240/5695 eff=42.3041% N=400
Z=-42.7(0.00%) | Like=-34.01..-7.29 [-34.3985..-21.0656] | it/evals=2250/5713 eff=42.3490% N=400
Z=-40.7(0.00%) | Like=-31.66..-7.29 [-34.3985..-21.0656] | it/evals=2280/5747 eff=42.6407% N=400
Z=-38.0(0.00%) | Like=-28.80..-7.29 [-34.3985..-21.0656] | it/evals=2320/5804 eff=42.9312% N=400
Z=-36.7(0.00%) | Like=-27.69..-7.29 [-34.3985..-21.0656] | it/evals=2340/5836 eff=43.0464% N=400
Z=-35.6(0.00%) | Like=-26.49..-7.29 [-34.3985..-21.0656] | it/evals=2360/5858 eff=43.2393% N=400
Z=-33.5(0.00%) | Like=-24.58..-7.29 [-34.3985..-21.0656] | it/evals=2400/5919 eff=43.4861% N=400
Z=-32.2(0.00%) | Like=-23.30..-7.29 [-34.3985..-21.0656] | it/evals=2430/5960 eff=43.7050% N=400
Z=-31.8(0.00%) | Like=-22.82..-7.29 [-34.3985..-21.0656] | it/evals=2440/5974 eff=43.7747% N=400
Z=-30.5(0.00%) | Like=-21.84..-7.29 [-34.3985..-21.0656] | it/evals=2480/6022 eff=44.1124% N=400
Z=-29.2(0.00%) | Like=-20.52..-7.29 [-21.0604..-15.1647] | it/evals=2520/6083 eff=44.3428% N=400
Z=-28.3(0.00%) | Like=-19.50..-7.29 [-21.0604..-15.1647] | it/evals=2560/6132 eff=44.6615% N=400
Z=-27.2(0.00%) | Like=-18.44..-7.29 [-21.0604..-15.1647] | it/evals=2600/6182 eff=44.9671% N=400
Z=-27.0(0.00%) | Like=-18.20..-7.29 [-21.0604..-15.1647] | it/evals=2610/6197 eff=45.0233% N=400
Z=-26.3(0.00%) | Like=-17.43..-7.29 [-21.0604..-15.1647] | it/evals=2640/6232 eff=45.2675% N=400
Z=-25.4(0.01%) | Like=-16.61..-7.29 [-21.0604..-15.1647] | it/evals=2680/6289 eff=45.5086% N=400
Z=-25.0(0.01%) | Like=-15.99..-7.24 [-21.0604..-15.1647] | it/evals=2700/6321 eff=45.6004% N=400
Z=-24.5(0.02%) | Like=-15.58..-7.24 [-21.0604..-15.1647] | it/evals=2720/6342 eff=45.7758% N=400
Z=-23.7(0.05%) | Like=-14.79..-7.24 [-15.1427..-14.5262] | it/evals=2760/6390 eff=46.0768% N=400
Z=-23.2(0.09%) | Like=-14.21..-7.24 [-14.2163..-14.2061] | it/evals=2790/6426 eff=46.2994% N=400
Z=-23.0(0.10%) | Like=-13.97..-7.24 [-13.9861..-13.9660] | it/evals=2800/6442 eff=46.3423% N=400
Z=-22.3(0.21%) | Like=-13.27..-7.24 [-13.2741..-13.2669]*| it/evals=2840/6499 eff=46.5650% N=400
Z=-21.7(0.39%) | Like=-12.76..-7.24 [-12.8329..-12.7643] | it/evals=2880/6556 eff=46.7836% N=400
Z=-21.1(0.68%) | Like=-12.12..-7.24 [-12.1197..-12.1097]*| it/evals=2920/6607 eff=47.0437% N=400
Z=-20.6(1.14%) | Like=-11.62..-7.24 [-11.6168..-11.5897] | it/evals=2960/6664 eff=47.2542% N=400
Z=-20.5(1.28%) | Like=-11.50..-7.24 [-11.4994..-11.4747] | it/evals=2970/6684 eff=47.2629% N=400
Z=-20.1(1.82%) | Like=-11.13..-7.24 [-11.1522..-11.1325] | it/evals=3000/6719 eff=47.4759% N=400
Z=-19.7(2.70%) | Like=-10.74..-7.24 [-10.7423..-10.7081] | it/evals=3040/6771 eff=47.7162% N=400
Z=-19.5(3.26%) | Like=-10.58..-7.24 [-10.5844..-10.5801]*| it/evals=3060/6796 eff=47.8424% N=400
Z=-19.4(3.84%) | Like=-10.47..-7.24 [-10.4732..-10.4718]*| it/evals=3080/6819 eff=47.9826% N=400
Z=-19.0(5.24%) | Like=-10.12..-7.24 [-10.1229..-10.1112] | it/evals=3120/6872 eff=48.2077% N=400
Z=-18.8(6.50%) | Like=-9.90..-7.24 [-9.9049..-9.9044]*| it/evals=3150/6910 eff=48.3871% N=400
Z=-18.8(6.93%) | Like=-9.85..-7.24 [-9.8493..-9.8478]*| it/evals=3160/6921 eff=48.4588% N=400
Z=-18.5(8.98%) | Like=-9.63..-7.24 [-9.6282..-9.6175] | it/evals=3200/6979 eff=48.6396% N=400
Z=-18.4(10.19%) | Like=-9.48..-7.24 [-9.4793..-9.4740]*| it/evals=3221/7010 eff=48.7292% N=400
Z=-18.4(10.37%) | Like=-9.46..-7.24 [-9.4645..-9.4645]*| it/evals=3224/7014 eff=48.7451% N=400
Z=-18.3(11.44%) | Like=-9.39..-7.24 [-9.3912..-9.3874]*| it/evals=3240/7040 eff=48.7952% N=400
Z=-18.1(13.92%) | Like=-9.23..-7.24 [-9.2307..-9.2292]*| it/evals=3280/7094 eff=48.9991% N=400
Z=-18.0(15.46%) | Like=-9.10..-7.24 [-9.1001..-9.0956]*| it/evals=3304/7124 eff=49.1374% N=400
Z=-17.9(16.57%) | Like=-8.99..-7.24 [-9.0106..-8.9925] | it/evals=3320/7150 eff=49.1852% N=400
Z=-17.8(17.32%) | Like=-8.92..-7.24 [-8.9204..-8.9154]*| it/evals=3330/7171 eff=49.1803% N=400
Z=-17.7(19.76%) | Like=-8.82..-7.24 [-8.8190..-8.8154]*| it/evals=3360/7207 eff=49.3610% N=400
Z=-17.6(22.97%) | Like=-8.68..-7.24 [-8.6817..-8.6793]*| it/evals=3400/7267 eff=49.5122% N=400
Z=-17.5(24.79%) | Like=-8.60..-7.24 [-8.6025..-8.5992]*| it/evals=3420/7294 eff=49.6084% N=400
Z=-17.4(26.55%) | Like=-8.51..-7.24 [-8.5122..-8.5081]*| it/evals=3440/7321 eff=49.7038% N=400
Z=-17.3(30.37%) | Like=-8.38..-7.24 [-8.3798..-8.3747]*| it/evals=3480/7367 eff=49.9498% N=400
Z=-17.2(33.21%) | Like=-8.29..-7.24 [-8.2911..-8.2825]*| it/evals=3510/7414 eff=50.0428% N=400
Z=-17.2(34.12%) | Like=-8.26..-7.24 [-8.2622..-8.2602]*| it/evals=3520/7430 eff=50.0711% N=400
Z=-17.1(37.84%) | Like=-8.18..-7.24 [-8.1755..-8.1742]*| it/evals=3560/7481 eff=50.2754% N=400
Z=-17.0(41.47%) | Like=-8.07..-7.24 [-8.0732..-8.0708]*| it/evals=3600/7532 eff=50.4767% N=400
Z=-16.9(45.27%) | Like=-8.01..-7.24 [-8.0074..-8.0044]*| it/evals=3640/7586 eff=50.6540% N=400
Z=-16.8(48.87%) | Like=-7.93..-7.24 [-7.9329..-7.9288]*| it/evals=3680/7651 eff=50.7516% N=400
Z=-16.8(49.80%) | Like=-7.91..-7.24 [-7.9107..-7.9107]*| it/evals=3690/7671 eff=50.7496% N=400
[ultranest] Explored until L=-7
[ultranest] Likelihood function evaluations: 7674
[ultranest]   logZ = -16.07 +- 0.1019
[ultranest] Effective samples strategy satisfied (ESS = 975.1, need >400)
[ultranest] Posterior uncertainty strategy is satisfied (KL: 0.45+-0.07 nat, need <0.50 nat)
[ultranest] Evidency uncertainty strategy is satisfied (dlogz=0.42, need <0.5)
[ultranest]   logZ error budget: single: 0.14 bs:0.10 tail:0.41 total:0.42 required:<0.50
[ultranest] done iterating.
23:24:01 INFO      fit restored to maximum of posterior                                         sampler_base.py:178
         INFO      fit restored to maximum of posterior                                         sampler_base.py:178
Maximum a posteriori probability (MAP) point:

result unit
parameter
demo.spectrum.main.Sin.K (9.91 +/- 0.18) x 10^-1 1 / (cm2 keV s)
demo.spectrum.main.Sin.f (1.001 -0.006 +0.005) x 10^-1 rad / keV
Values of -log(posterior) at the minimum:

-log(posterior)
demo -7.228538
total -7.228538
Values of statistical measures:

statistical measures
AIC 19.162958
BIC 20.448540
DIC 18.367390
PDIC 1.957350
log(Z) -6.989315
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../_images/notebooks_sampler_docs_16_149.png
../_images/notebooks_sampler_docs_16_150.png
../_images/notebooks_sampler_docs_16_151.png