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()

22:18:38 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.

22:18:39 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))

22:18:41 INFO      Using Gaussian statistic (equivalent to chi^2) with the provided errors.            XYLike.py:93

22:18:42 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

22:18:46 INFO      Mean acceptance fraction: 0.7144                                            emcee_sampler.py:157

22:18:47 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 -0.16 +0.15) x 10^-1	1 / (cm2 keV s)
demo.spectrum.main.Sin.f	(9.99 -0.05 +0.06) x 10^-2	rad / keV

Values of -log(posterior) at the minimum:

	-log(posterior)
demo	-6.598494
total	-6.598494

Values of statistical measures:

	statistical measures
AIC	17.902870
BIC	19.188452
DIC	17.239380
PDIC	2.017942

[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()

22:18:48 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)=  -15.697095151737290      +/-  0.14206543454228004
 Total Likelihood Evaluations:         6722
 Sampling finished. Exiting MultiNest

22:18:50 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 +/- 0.16) x 10^-1	1 / (cm2 keV s)
demo.spectrum.main.Sin.f	(10.00 +/- 0.05) x 10^-2	rad / keV

Values of -log(posterior) at the minimum:

	-log(posterior)
demo	-6.599193
total	-6.599193

Values of statistical measures:

	statistical measures
AIC	17.904268
BIC	19.189851
DIC	17.356304
PDIC	2.078925
log(Z)	-6.817162

         INFO      deleting the chain directory chains                                     multinest_sampler.py:255

[6]:

../_images/notebooks_sampler_docs_9_12.png

../_images/notebooks_sampler_docs_9_13.png

../_images/notebooks_sampler_docs_9_14.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()

22:18:51 INFO      sampler set to dynesty_nested                                           bayesian_analysis.py:202

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3658it [00:06, 805.88it/s, bound: 7 | nc: 6 | ncall: 18034 | eff(%): 20.284 | loglstar: -inf < -7.845 < inf | logz: -17.143 +/- 0.144 | dlogz: 1.626 > 0.409]: end{sphinxVerbatim}

3770it [00:06, 876.19it/s, bound: 7 | nc: 2 | ncall: 18259 | eff(%): 20.647 | loglstar: -inf < -7.533 < inf | logz: -16.853 +/- 0.144 | dlogz: 1.196 > 0.409]: </pre>
3770it [00:06, 876.19it/s, bound: 7 | nc: 2 | ncall: 18259 | eff(%): 20.647 | loglstar: -inf < -7.533 < inf | logz: -16.853 +/- 0.144 | dlogz: 1.196 > 0.409]: end{sphinxVerbatim}

3873it [00:06, 664.96it/s, bound: 8 | nc: 1 | ncall: 18441 | eff(%): 21.002 | loglstar: -inf < -7.312 < inf | logz: -16.645 +/- 0.144 | dlogz: 0.896 > 0.409]: </pre>
3873it [00:06, 664.96it/s, bound: 8 | nc: 1 | ncall: 18441 | eff(%): 21.002 | loglstar: -inf < -7.312 < inf | logz: -16.645 +/- 0.144 | dlogz: 0.896 > 0.409]: end{sphinxVerbatim}

4048it [00:06, 882.23it/s, bound: 8 | nc: 1 | ncall: 18720 | eff(%): 21.624 | loglstar: -inf < -7.092 < inf | logz: -16.395 +/- 0.144 | dlogz: 0.547 > 0.409]: </pre>
4048it [00:06, 882.23it/s, bound: 8 | nc: 1 | ncall: 18720 | eff(%): 21.624 | loglstar: -inf < -7.092 < inf | logz: -16.395 +/- 0.144 | dlogz: 0.547 > 0.409]: end{sphinxVerbatim}

4153it [00:06, 611.51it/s, +400 | bound: 8 | nc: 1 | ncall: 19322 | eff(%): 24.062 | loglstar: -inf < -6.608 < inf | logz: -15.942 +/- 0.144 | dlogz: 0.001 > 0.409]: </pre>
4153it [00:06, 611.51it/s, +400 | bound: 8 | nc: 1 | ncall: 19322 | eff(%): 24.062 | loglstar: -inf < -6.608 < inf | logz: -15.942 +/- 0.144 | dlogz: 0.001 > 0.409]: end{sphinxVerbatim}

22:18:59 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 +/- 0.16) x 10^-1	1 / (cm2 keV s)
demo.spectrum.main.Sin.f	(9.99 +/- 0.05) x 10^-2	rad / keV

Values of -log(posterior) at the minimum:

	-log(posterior)
demo	-6.598725
total	-6.598725

Values of statistical measures:

	statistical measures
AIC	17.903332
BIC	19.188914
DIC	17.335774
PDIC	2.068719
log(Z)	-6.923581

[7]:

../_images/notebooks_sampler_docs_11_52.png

../_images/notebooks_sampler_docs_11_53.png

../_images/notebooks_sampler_docs_11_54.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()

22:19:00 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]

1it [00:00, 7.81it/s, batch: 0 | bound: 0 | nc: 1 | ncall: 1 | eff(%): 0.200 | loglstar: -inf < -9730.319 < inf | logz: -9737.229 +/- 0.117 | dlogz: inf > 0.010]: </pre>
1it [00:00, 7.81it/s, batch: 0 | bound: 0 | nc: 1 | ncall: 1 | eff(%): 0.200 | loglstar: -inf < -9730.319 < inf | logz: -9737.229 +/- 0.117 | dlogz: inf > 0.010]: end{sphinxVerbatim}

113it [00:00, 593.49it/s, batch: 0 | bound: 0 | nc: 1 | ncall: 122 | eff(%): 18.167 | loglstar: -inf < -5080.547 < inf | logz: -5087.674 +/- 0.119 | dlogz: 5070.630 > 0.010]: </pre>
113it [00:00, 593.49it/s, batch: 0 | bound: 0 | nc: 1 | ncall: 122 | eff(%): 18.167 | loglstar: -inf < -5080.547 < inf | logz: -5087.674 +/- 0.119 | dlogz: 5070.630 > 0.010]: end{sphinxVerbatim}

242it [00:00, 892.34it/s, batch: 0 | bound: 0 | nc: 1 | ncall: 306 | eff(%): 30.025 | loglstar: -inf < -3801.351 < inf | logz: -3808.742 +/- 0.121 | dlogz: 3808.676 > 0.010]: </pre>
242it [00:00, 892.34it/s, batch: 0 | bound: 0 | nc: 1 | ncall: 306 | eff(%): 30.025 | loglstar: -inf < -3801.351 < inf | logz: -3808.742 +/- 0.121 | dlogz: 3808.676 > 0.010]: end{sphinxVerbatim}

337it [00:00, 865.98it/s, batch: 0 | bound: 0 | nc: 1 | ncall: 460 | eff(%): 35.104 | loglstar: -inf < -3336.960 < inf | logz: -3343.678 +/- 0.110 | dlogz: 3335.811 > 0.010]: </pre>
337it [00:00, 865.98it/s, batch: 0 | bound: 0 | nc: 1 | ncall: 460 | eff(%): 35.104 | loglstar: -inf < -3336.960 < inf | logz: -3343.678 +/- 0.110 | dlogz: 3335.811 > 0.010]: end{sphinxVerbatim}

473it [00:00, 1032.56it/s, batch: 0 | bound: 0 | nc: 2 | ncall: 751 | eff(%): 37.810 | loglstar: -inf < -2915.463 < inf | logz: -2921.918 +/- 0.110 | dlogz: 2913.418 > 0.010]: </pre>
473it [00:00, 1032.56it/s, batch: 0 | bound: 0 | nc: 2 | ncall: 751 | eff(%): 37.810 | loglstar: -inf < -2915.463 < inf | logz: -2921.918 +/- 0.110 | dlogz: 2913.418 > 0.010]: end{sphinxVerbatim}

580it [00:00, 905.09it/s, batch: 0 | bound: 0 | nc: 2 | ncall: 1022 | eff(%): 38.108 | loglstar: -inf < -2593.152 < inf | logz: -2600.827 +/- 0.118 | dlogz: 2594.527 > 0.010]: </pre>
580it [00:00, 905.09it/s, batch: 0 | bound: 0 | nc: 2 | ncall: 1022 | eff(%): 38.108 | loglstar: -inf < -2593.152 < inf | logz: -2600.827 +/- 0.118 | dlogz: 2594.527 > 0.010]: end{sphinxVerbatim}

685it [00:00, 945.53it/s, batch: 0 | bound: 0 | nc: 1 | ncall: 1397 | eff(%): 36.110 | loglstar: -inf < -2337.326 < inf | logz: -2345.590 +/- 0.128 | dlogz: 2342.345 > 0.010]: </pre>
685it [00:00, 945.53it/s, batch: 0 | bound: 0 | nc: 1 | ncall: 1397 | eff(%): 36.110 | loglstar: -inf < -2337.326 < inf | logz: -2345.590 +/- 0.128 | dlogz: 2342.345 > 0.010]: end{sphinxVerbatim}

784it [00:01, 655.59it/s, batch: 0 | bound: 0 | nc: 2 | ncall: 1860 | eff(%): 33.220 | loglstar: -inf < -2153.064 < inf | logz: -2161.455 +/- 0.127 | dlogz: 2156.069 > 0.010]: </pre>
784it [00:01, 655.59it/s, batch: 0 | bound: 0 | nc: 2 | ncall: 1860 | eff(%): 33.220 | loglstar: -inf < -2153.064 < inf | logz: -2161.455 +/- 0.127 | dlogz: 2156.069 > 0.010]: end{sphinxVerbatim}

864it [00:01, 680.34it/s, batch: 0 | bound: 0 | nc: 1 | ncall: 2254 | eff(%): 31.373 | loglstar: -inf < -2008.775 < inf | logz: -2016.491 +/- 0.118 | dlogz: 2008.928 > 0.010]: </pre>
864it [00:01, 680.34it/s, batch: 0 | bound: 0 | nc: 1 | ncall: 2254 | eff(%): 31.373 | loglstar: -inf < -2008.775 < inf | logz: -2016.491 +/- 0.118 | dlogz: 2008.928 > 0.010]: end{sphinxVerbatim}

943it [00:01, 690.18it/s, batch: 0 | bound: 0 | nc: 9 | ncall: 2648 | eff(%): 29.956 | loglstar: -inf < -1931.436 < inf | logz: -1938.188 +/- 0.110 | dlogz: 1929.962 > 0.010]: </pre>
943it [00:01, 690.18it/s, batch: 0 | bound: 0 | nc: 9 | ncall: 2648 | eff(%): 29.956 | loglstar: -inf < -1931.436 < inf | logz: -1938.188 +/- 0.110 | dlogz: 1929.962 > 0.010]: end{sphinxVerbatim}

1020it [00:01, 652.97it/s, batch: 0 | bound: 0 | nc: 5 | ncall: 3127 | eff(%): 28.122 | loglstar: -inf < -1610.162 < inf | logz: -1619.108 +/- 0.134 | dlogz: 1626.459 > 0.010]: </pre>
1020it [00:01, 652.97it/s, batch: 0 | bound: 0 | nc: 5 | ncall: 3127 | eff(%): 28.122 | loglstar: -inf < -1610.162 < inf | logz: -1619.108 +/- 0.134 | dlogz: 1626.459 > 0.010]: end{sphinxVerbatim}

1091it [00:01, 636.18it/s, batch: 0 | bound: 0 | nc: 3 | ncall: 3599 | eff(%): 26.616 | loglstar: -inf < -1351.994 < inf | logz: -1360.769 +/- 0.126 | dlogz: 1353.604 > 0.010]: </pre>
1091it [00:01, 636.18it/s, batch: 0 | bound: 0 | nc: 3 | ncall: 3599 | eff(%): 26.616 | loglstar: -inf < -1351.994 < inf | logz: -1360.769 +/- 0.126 | dlogz: 1353.604 > 0.010]: end{sphinxVerbatim}

1159it [00:01, 579.75it/s, batch: 0 | bound: 0 | nc: 12 | ncall: 4195 | eff(%): 24.686 | loglstar: -inf < -1096.884 < inf | logz: -1106.107 +/- 0.136 | dlogz: 1105.564 > 0.010]: </pre>
1159it [00:01, 579.75it/s, batch: 0 | bound: 0 | nc: 12 | ncall: 4195 | eff(%): 24.686 | loglstar: -inf < -1096.884 < inf | logz: -1106.107 +/- 0.136 | dlogz: 1105.564 > 0.010]: end{sphinxVerbatim}

1220it [00:01, 541.08it/s, batch: 0 | bound: 0 | nc: 9 | ncall: 4899 | eff(%): 22.597 | loglstar: -inf < -907.924 < inf | logz: -916.564 +/- 0.127 | dlogz: 908.695 > 0.010]: </pre>
1220it [00:01, 541.08it/s, batch: 0 | bound: 0 | nc: 9 | ncall: 4899 | eff(%): 22.597 | loglstar: -inf < -907.924 < inf | logz: -916.564 +/- 0.127 | dlogz: 908.695 > 0.010]: end{sphinxVerbatim}

1277it [00:01, 469.90it/s, batch: 0 | bound: 0 | nc: 2 | ncall: 5640 | eff(%): 20.798 | loglstar: -inf < -788.123 < inf | logz: -796.019 +/- 0.120 | dlogz: 787.342 > 0.010]: </pre>
1277it [00:01, 469.90it/s, batch: 0 | bound: 0 | nc: 2 | ncall: 5640 | eff(%): 20.798 | loglstar: -inf < -788.123 < inf | logz: -796.019 +/- 0.120 | dlogz: 787.342 > 0.010]: end{sphinxVerbatim}

1327it [00:02, 449.02it/s, batch: 0 | bound: 0 | nc: 13 | ncall: 6158 | eff(%): 19.931 | loglstar: -inf < -686.807 < inf | logz: -695.597 +/- 0.127 | dlogz: 687.256 > 0.010]: </pre>
1327it [00:02, 449.02it/s, batch: 0 | bound: 0 | nc: 13 | ncall: 6158 | eff(%): 19.931 | loglstar: -inf < -686.807 < inf | logz: -695.597 +/- 0.127 | dlogz: 687.256 > 0.010]: end{sphinxVerbatim}

1374it [00:02, 438.54it/s, batch: 0 | bound: 0 | nc: 24 | ncall: 6791 | eff(%): 18.845 | loglstar: -inf < -612.067 < inf | logz: -621.603 +/- 0.135 | dlogz: 614.683 > 0.010]: </pre>
1374it [00:02, 438.54it/s, batch: 0 | bound: 0 | nc: 24 | ncall: 6791 | eff(%): 18.845 | loglstar: -inf < -612.067 < inf | logz: -621.603 +/- 0.135 | dlogz: 614.683 > 0.010]: end{sphinxVerbatim}

1419it [00:02, 432.53it/s, batch: 0 | bound: 0 | nc: 17 | ncall: 7445 | eff(%): 17.860 | loglstar: -inf < -542.056 < inf | logz: -550.805 +/- 0.124 | dlogz: 542.076 > 0.010]: </pre>
1419it [00:02, 432.53it/s, batch: 0 | bound: 0 | nc: 17 | ncall: 7445 | eff(%): 17.860 | loglstar: -inf < -542.056 < inf | logz: -550.805 +/- 0.124 | dlogz: 542.076 > 0.010]: end{sphinxVerbatim}

1463it [00:02, 353.00it/s, batch: 0 | bound: 0 | nc: 36 | ncall: 8325 | eff(%): 16.578 | loglstar: -inf < -493.076 < inf | logz: -502.111 +/- 0.127 | dlogz: 493.494 > 0.010]: </pre>
1463it [00:02, 353.00it/s, batch: 0 | bound: 0 | nc: 36 | ncall: 8325 | eff(%): 16.578 | loglstar: -inf < -493.076 < inf | logz: -502.111 +/- 0.127 | dlogz: 493.494 > 0.010]: end{sphinxVerbatim}

1501it [00:02, 268.52it/s, batch: 0 | bound: 0 | nc: 12 | ncall: 9091 | eff(%): 15.650 | loglstar: -inf < -456.489 < inf | logz: -465.994 +/- 0.131 | dlogz: 457.742 > 0.010]: </pre>
1501it [00:02, 268.52it/s, batch: 0 | bound: 0 | nc: 12 | ncall: 9091 | eff(%): 15.650 | loglstar: -inf < -456.489 < inf | logz: -465.994 +/- 0.131 | dlogz: 457.742 > 0.010]: end{sphinxVerbatim}

1532it [00:02, 246.44it/s, batch: 0 | bound: 0 | nc: 76 | ncall: 9848 | eff(%): 14.805 | loglstar: -inf < -434.093 < inf | logz: -442.667 +/- 0.124 | dlogz: 433.465 > 0.010]: </pre>
1532it [00:02, 246.44it/s, batch: 0 | bound: 0 | nc: 76 | ncall: 9848 | eff(%): 14.805 | loglstar: -inf < -434.093 < inf | logz: -442.667 +/- 0.124 | dlogz: 433.465 > 0.010]: end{sphinxVerbatim}

1560it [00:03, 237.30it/s, batch: 0 | bound: 0 | nc: 37 | ncall: 10488 | eff(%): 14.197 | loglstar: -inf < -413.986 < inf | logz: -422.557 +/- 0.125 | dlogz: 413.370 > 0.010]: </pre>
1560it [00:03, 237.30it/s, batch: 0 | bound: 0 | nc: 37 | ncall: 10488 | eff(%): 14.197 | loglstar: -inf < -413.986 < inf | logz: -422.557 +/- 0.125 | dlogz: 413.370 > 0.010]: end{sphinxVerbatim}

1586it [00:03, 207.64it/s, batch: 0 | bound: 0 | nc: 12 | ncall: 11141 | eff(%): 13.624 | loglstar: -inf < -398.893 < inf | logz: -406.994 +/- 0.122 | dlogz: 397.519 > 0.010]: </pre>
1586it [00:03, 207.64it/s, batch: 0 | bound: 0 | nc: 12 | ncall: 11141 | eff(%): 13.624 | loglstar: -inf < -398.893 < inf | logz: -406.994 +/- 0.122 | dlogz: 397.519 > 0.010]: end{sphinxVerbatim}

1609it [00:03, 187.84it/s, batch: 0 | bound: 0 | nc: 37 | ncall: 11940 | eff(%): 12.934 | loglstar: -inf < -383.916 < inf | logz: -393.003 +/- 0.129 | dlogz: 383.864 > 0.010]: </pre>
1609it [00:03, 187.84it/s, batch: 0 | bound: 0 | nc: 37 | ncall: 11940 | eff(%): 12.934 | loglstar: -inf < -383.916 < inf | logz: -393.003 +/- 0.129 | dlogz: 383.864 > 0.010]: end{sphinxVerbatim}

1629it [00:03, 189.32it/s, batch: 0 | bound: 0 | nc: 49 | ncall: 12404 | eff(%): 12.624 | loglstar: -inf < -368.271 < inf | logz: -377.174 +/- 0.128 | dlogz: 367.926 > 0.010]: </pre>
1629it [00:03, 189.32it/s, batch: 0 | bound: 0 | nc: 49 | ncall: 12404 | eff(%): 12.624 | loglstar: -inf < -368.271 < inf | logz: -377.174 +/- 0.128 | dlogz: 367.926 > 0.010]: end{sphinxVerbatim}

1649it [00:03, 188.16it/s, batch: 0 | bound: 0 | nc: 24 | ncall: 12948 | eff(%): 12.262 | loglstar: -inf < -354.622 < inf | logz: -363.851 +/- 0.126 | dlogz: 354.589 > 0.010]: </pre>
1649it [00:03, 188.16it/s, batch: 0 | bound: 0 | nc: 24 | ncall: 12948 | eff(%): 12.262 | loglstar: -inf < -354.622 < inf | logz: -363.851 +/- 0.126 | dlogz: 354.589 > 0.010]: end{sphinxVerbatim}

1669it [00:03, 150.80it/s, batch: 0 | bound: 0 | nc: 52 | ncall: 13406 | eff(%): 12.002 | loglstar: -inf < -342.563 < inf | logz: -351.078 +/- 0.126 | dlogz: 341.491 > 0.010]: </pre>
1669it [00:03, 150.80it/s, batch: 0 | bound: 0 | nc: 52 | ncall: 13406 | eff(%): 12.002 | loglstar: -inf < -342.563 < inf | logz: -351.078 +/- 0.126 | dlogz: 341.491 > 0.010]: end{sphinxVerbatim}

1695it [00:03, 172.02it/s, batch: 0 | bound: 0 | nc: 57 | ncall: 14082 | eff(%): 11.624 | loglstar: -inf < -328.462 < inf | logz: -337.273 +/- 0.125 | dlogz: 327.724 > 0.010]: </pre>
1695it [00:03, 172.02it/s, batch: 0 | bound: 0 | nc: 57 | ncall: 14082 | eff(%): 11.624 | loglstar: -inf < -328.462 < inf | logz: -337.273 +/- 0.125 | dlogz: 327.724 > 0.010]: end{sphinxVerbatim}

1718it [00:04, 184.08it/s, batch: 0 | bound: 0 | nc: 13 | ncall: 14641 | eff(%): 11.347 | loglstar: -inf < -316.280 < inf | logz: -325.024 +/- 0.127 | dlogz: 315.394 > 0.010]: </pre>
1718it [00:04, 184.08it/s, batch: 0 | bound: 0 | nc: 13 | ncall: 14641 | eff(%): 11.347 | loglstar: -inf < -316.280 < inf | logz: -325.024 +/- 0.127 | dlogz: 315.394 > 0.010]: end{sphinxVerbatim}

1738it [00:04, 153.34it/s, batch: 0 | bound: 0 | nc: 134 | ncall: 15722 | eff(%): 10.714 | loglstar: -inf < -308.130 < inf | logz: -317.159 +/- 0.128 | dlogz: 307.722 > 0.010]: </pre>
1738it [00:04, 153.34it/s, batch: 0 | bound: 0 | nc: 134 | ncall: 15722 | eff(%): 10.714 | loglstar: -inf < -308.130 < inf | logz: -317.159 +/- 0.128 | dlogz: 307.722 > 0.010]: end{sphinxVerbatim}

1756it [00:04, 145.97it/s, batch: 0 | bound: 0 | nc: 31 | ncall: 16474 | eff(%): 10.345 | loglstar: -inf < -300.709 < inf | logz: -309.566 +/- 0.125 | dlogz: 299.845 > 0.010]: </pre>
1756it [00:04, 145.97it/s, batch: 0 | bound: 0 | nc: 31 | ncall: 16474 | eff(%): 10.345 | loglstar: -inf < -300.709 < inf | logz: -309.566 +/- 0.125 | dlogz: 299.845 > 0.010]: end{sphinxVerbatim}

1772it [00:04, 126.42it/s, batch: 0 | bound: 0 | nc: 13 | ncall: 17213 | eff(%): 10.004 | loglstar: -inf < -292.034 < inf | logz: -301.281 +/- 0.127 | dlogz: 291.687 > 0.010]: </pre>
1772it [00:04, 126.42it/s, batch: 0 | bound: 0 | nc: 13 | ncall: 17213 | eff(%): 10.004 | loglstar: -inf < -292.034 < inf | logz: -301.281 +/- 0.127 | dlogz: 291.687 > 0.010]: end{sphinxVerbatim}

1786it [00:04, 104.43it/s, batch: 0 | bound: 1 | nc: 1 | ncall: 17263 | eff(%): 10.055 | loglstar: -inf < -282.299 < inf | logz: -291.715 +/- 0.133 | dlogz: 282.441 > 0.010]: </pre>
1786it [00:04, 104.43it/s, batch: 0 | bound: 1 | nc: 1 | ncall: 17263 | eff(%): 10.055 | loglstar: -inf < -282.299 < inf | logz: -291.715 +/- 0.133 | dlogz: 282.441 > 0.010]: end{sphinxVerbatim}

1945it [00:04, 399.57it/s, batch: 0 | bound: 1 | nc: 1 | ncall: 17479 | eff(%): 10.818 | loglstar: -inf < -215.012 < inf | logz: -224.246 +/- 0.128 | dlogz: 214.189 > 0.010]: </pre>
1945it [00:04, 399.57it/s, batch: 0 | bound: 1 | nc: 1 | ncall: 17479 | eff(%): 10.818 | loglstar: -inf < -215.012 < inf | logz: -224.246 +/- 0.128 | dlogz: 214.189 > 0.010]: end{sphinxVerbatim}

2052it [00:04, 546.60it/s, batch: 0 | bound: 1 | nc: 3 | ncall: 17652 | eff(%): 11.305 | loglstar: -inf < -172.242 < inf | logz: -181.162 +/- 0.129 | dlogz: 170.684 > 0.010]: </pre>
2052it [00:04, 546.60it/s, batch: 0 | bound: 1 | nc: 3 | ncall: 17652 | eff(%): 11.305 | loglstar: -inf < -172.242 < inf | logz: -181.162 +/- 0.129 | dlogz: 170.684 > 0.010]: end{sphinxVerbatim}

2183it [00:05, 727.13it/s, batch: 0 | bound: 1 | nc: 8 | ncall: 17958 | eff(%): 11.827 | loglstar: -inf < -137.814 < inf | logz: -147.110 +/- 0.127 | dlogz: 136.396 > 0.010]: </pre>
2183it [00:05, 727.13it/s, batch: 0 | bound: 1 | nc: 8 | ncall: 17958 | eff(%): 11.827 | loglstar: -inf < -137.814 < inf | logz: -147.110 +/- 0.127 | dlogz: 136.396 > 0.010]: end{sphinxVerbatim}

2272it [00:05, 565.49it/s, batch: 0 | bound: 2 | nc: 1 | ncall: 18081 | eff(%): 12.228 | loglstar: -inf < -118.898 < inf | logz: -127.978 +/- 0.129 | dlogz: 117.020 > 0.010]: </pre>
2272it [00:05, 565.49it/s, batch: 0 | bound: 2 | nc: 1 | ncall: 18081 | eff(%): 12.228 | loglstar: -inf < -118.898 < inf | logz: -127.978 +/- 0.129 | dlogz: 117.020 > 0.010]: end{sphinxVerbatim}

2378it [00:05, 554.25it/s, batch: 0 | bound: 2 | nc: 1 | ncall: 18216 | eff(%): 12.706 | loglstar: -inf < -101.052 < inf | logz: -110.581 +/- 0.128 | dlogz: 99.414 > 0.010]: </pre>
2378it [00:05, 554.25it/s, batch: 0 | bound: 2 | nc: 1 | ncall: 18216 | eff(%): 12.706 | loglstar: -inf < -101.052 < inf | logz: -110.581 +/- 0.128 | dlogz: 99.414 > 0.010]: end{sphinxVerbatim}

2505it [00:05, 696.96it/s, batch: 0 | bound: 2 | nc: 5 | ncall: 18430 | eff(%): 13.233 | loglstar: -inf < -77.910 < inf | logz: -87.176 +/- 0.128 | dlogz: 75.695 > 0.010]: </pre>
2505it [00:05, 696.96it/s, batch: 0 | bound: 2 | nc: 5 | ncall: 18430 | eff(%): 13.233 | loglstar: -inf < -77.910 < inf | logz: -87.176 +/- 0.128 | dlogz: 75.695 > 0.010]: end{sphinxVerbatim}

2610it [00:05, 774.79it/s, batch: 0 | bound: 2 | nc: 2 | ncall: 18662 | eff(%): 13.621 | loglstar: -inf < -66.910 < inf | logz: -75.557 +/- 0.125 | dlogz: 63.777 > 0.010]: </pre>
2610it [00:05, 774.79it/s, batch: 0 | bound: 2 | nc: 2 | ncall: 18662 | eff(%): 13.621 | loglstar: -inf < -66.910 < inf | logz: -75.557 +/- 0.125 | dlogz: 63.777 > 0.010]: end{sphinxVerbatim}

2701it [00:06, 516.58it/s, batch: 0 | bound: 3 | nc: 2 | ncall: 18819 | eff(%): 13.981 | loglstar: -inf < -57.586 < inf | logz: -67.174 +/- 0.127 | dlogz: 55.259 > 0.010]: </pre>
2701it [00:06, 516.58it/s, batch: 0 | bound: 3 | nc: 2 | ncall: 18819 | eff(%): 13.981 | loglstar: -inf < -57.586 < inf | logz: -67.174 +/- 0.127 | dlogz: 55.259 > 0.010]: end{sphinxVerbatim}

2844it [00:06, 680.65it/s, batch: 0 | bound: 3 | nc: 1 | ncall: 19015 | eff(%): 14.573 | loglstar: -inf < -43.104 < inf | logz: -52.490 +/- 0.130 | dlogz: 40.265 > 0.010]: </pre>
2844it [00:06, 680.65it/s, batch: 0 | bound: 3 | nc: 1 | ncall: 19015 | eff(%): 14.573 | loglstar: -inf < -43.104 < inf | logz: -52.490 +/- 0.130 | dlogz: 40.265 > 0.010]: end{sphinxVerbatim}

2986it [00:06, 830.88it/s, batch: 0 | bound: 3 | nc: 4 | ncall: 19277 | eff(%): 15.098 | loglstar: -inf < -34.120 < inf | logz: -43.453 +/- 0.128 | dlogz: 30.920 > 0.010]: </pre>
2986it [00:06, 830.88it/s, batch: 0 | bound: 3 | nc: 4 | ncall: 19277 | eff(%): 15.098 | loglstar: -inf < -34.120 < inf | logz: -43.453 +/- 0.128 | dlogz: 30.920 > 0.010]: end{sphinxVerbatim}

3094it [00:06, 610.01it/s, batch: 0 | bound: 4 | nc: 1 | ncall: 19527 | eff(%): 15.449 | loglstar: -inf < -28.551 < inf | logz: -38.020 +/- 0.130 | dlogz: 25.269 > 0.010]: </pre>
3094it [00:06, 610.01it/s, batch: 0 | bound: 4 | nc: 1 | ncall: 19527 | eff(%): 15.449 | loglstar: -inf < -28.551 < inf | logz: -38.020 +/- 0.130 | dlogz: 25.269 > 0.010]: end{sphinxVerbatim}

3218it [00:06, 723.75it/s, batch: 0 | bound: 4 | nc: 1 | ncall: 19675 | eff(%): 15.950 | loglstar: -inf < -24.292 < inf | logz: -33.556 +/- 0.128 | dlogz: 20.550 > 0.010]: </pre>
3218it [00:06, 723.75it/s, batch: 0 | bound: 4 | nc: 1 | ncall: 19675 | eff(%): 15.950 | loglstar: -inf < -24.292 < inf | logz: -33.556 +/- 0.128 | dlogz: 20.550 > 0.010]: end{sphinxVerbatim}

3332it [00:06, 807.85it/s, batch: 0 | bound: 4 | nc: 3 | ncall: 19849 | eff(%): 16.374 | loglstar: -inf < -20.661 < inf | logz: -29.950 +/- 0.128 | dlogz: 16.710 > 0.010]: </pre>
3332it [00:06, 807.85it/s, batch: 0 | bound: 4 | nc: 3 | ncall: 19849 | eff(%): 16.374 | loglstar: -inf < -20.661 < inf | logz: -29.950 +/- 0.128 | dlogz: 16.710 > 0.010]: end{sphinxVerbatim}

3464it [00:06, 923.55it/s, batch: 0 | bound: 4 | nc: 1 | ncall: 20108 | eff(%): 16.809 | loglstar: -inf < -17.694 < inf | logz: -26.931 +/- 0.128 | dlogz: 13.420 > 0.010]: </pre>
3464it [00:06, 923.55it/s, batch: 0 | bound: 4 | nc: 1 | ncall: 20108 | eff(%): 16.809 | loglstar: -inf < -17.694 < inf | logz: -26.931 +/- 0.128 | dlogz: 13.420 > 0.010]: end{sphinxVerbatim}

3575it [00:07, 635.63it/s, batch: 0 | bound: 5 | nc: 1 | ncall: 20305 | eff(%): 17.183 | loglstar: -inf < -15.615 < inf | logz: -24.865 +/- 0.129 | dlogz: 11.129 > 0.010]: </pre>
3575it [00:07, 635.63it/s, batch: 0 | bound: 5 | nc: 1 | ncall: 20305 | eff(%): 17.183 | loglstar: -inf < -15.615 < inf | logz: -24.865 +/- 0.129 | dlogz: 11.129 > 0.010]: end{sphinxVerbatim}

3696it [00:07, 742.07it/s, batch: 0 | bound: 5 | nc: 1 | ncall: 20468 | eff(%): 17.627 | loglstar: -inf < -13.534 < inf | logz: -22.945 +/- 0.129 | dlogz: 8.966 > 0.010]: </pre>
3696it [00:07, 742.07it/s, batch: 0 | bound: 5 | nc: 1 | ncall: 20468 | eff(%): 17.627 | loglstar: -inf < -13.534 < inf | logz: -22.945 +/- 0.129 | dlogz: 8.966 > 0.010]: end{sphinxVerbatim}

3828it [00:07, 862.92it/s, batch: 0 | bound: 5 | nc: 2 | ncall: 20695 | eff(%): 18.061 | loglstar: -inf < -11.966 < inf | logz: -21.271 +/- 0.129 | dlogz: 7.024 > 0.010]: </pre>
3828it [00:07, 862.92it/s, batch: 0 | bound: 5 | nc: 2 | ncall: 20695 | eff(%): 18.061 | loglstar: -inf < -11.966 < inf | logz: -21.271 +/- 0.129 | dlogz: 7.024 > 0.010]: end{sphinxVerbatim}

3963it [00:07, 975.31it/s, batch: 0 | bound: 5 | nc: 4 | ncall: 20981 | eff(%): 18.449 | loglstar: -inf < -10.793 < inf | logz: -20.070 +/- 0.129 | dlogz: 5.554 > 0.010]: </pre>
3963it [00:07, 975.31it/s, batch: 0 | bound: 5 | nc: 4 | ncall: 20981 | eff(%): 18.449 | loglstar: -inf < -10.793 < inf | logz: -20.070 +/- 0.129 | dlogz: 5.554 > 0.010]: end{sphinxVerbatim}

4080it [00:07, 733.93it/s, batch: 0 | bound: 6 | nc: 1 | ncall: 21134 | eff(%): 18.859 | loglstar: -inf < -9.762 < inf | logz: -19.212 +/- 0.129 | dlogz: 4.469 > 0.010]: </pre>
4080it [00:07, 733.93it/s, batch: 0 | bound: 6 | nc: 1 | ncall: 21134 | eff(%): 18.859 | loglstar: -inf < -9.762 < inf | logz: -19.212 +/- 0.129 | dlogz: 4.469 > 0.010]: end{sphinxVerbatim}

4231it [00:07, 890.85it/s, batch: 0 | bound: 6 | nc: 2 | ncall: 21414 | eff(%): 19.307 | loglstar: -inf < -8.831 < inf | logz: -18.255 +/- 0.130 | dlogz: 3.237 > 0.010]: </pre>
4231it [00:07, 890.85it/s, batch: 0 | bound: 6 | nc: 2 | ncall: 21414 | eff(%): 19.307 | loglstar: -inf < -8.831 < inf | logz: -18.255 +/- 0.130 | dlogz: 3.237 > 0.010]: end{sphinxVerbatim}

4343it [00:07, 886.09it/s, batch: 0 | bound: 6 | nc: 2 | ncall: 21669 | eff(%): 19.590 | loglstar: -inf < -8.384 < inf | logz: -17.743 +/- 0.130 | dlogz: 2.542 > 0.010]: </pre>
4343it [00:07, 886.09it/s, batch: 0 | bound: 6 | nc: 2 | ncall: 21669 | eff(%): 19.590 | loglstar: -inf < -8.384 < inf | logz: -17.743 +/- 0.130 | dlogz: 2.542 > 0.010]: end{sphinxVerbatim}

4448it [00:08, 511.59it/s, batch: 0 | bound: 7 | nc: 1 | ncall: 21850 | eff(%): 19.902 | loglstar: -inf < -8.020 < inf | logz: -17.376 +/- 0.129 | dlogz: 2.023 > 0.010]: </pre>
4448it [00:08, 511.59it/s, batch: 0 | bound: 7 | nc: 1 | ncall: 21850 | eff(%): 19.902 | loglstar: -inf < -8.020 < inf | logz: -17.376 +/- 0.129 | dlogz: 2.023 > 0.010]: end{sphinxVerbatim}

4529it [00:08, 349.32it/s, batch: 0 | bound: 7 | nc: 1 | ncall: 21966 | eff(%): 20.159 | loglstar: -inf < -7.766 < inf | logz: -17.132 +/- 0.129 | dlogz: 1.681 > 0.010]: </pre>
4529it [00:08, 349.32it/s, batch: 0 | bound: 7 | nc: 1 | ncall: 21966 | eff(%): 20.159 | loglstar: -inf < -7.766 < inf | logz: -17.132 +/- 0.129 | dlogz: 1.681 > 0.010]: end{sphinxVerbatim}

4672it [00:08, 480.71it/s, batch: 0 | bound: 7 | nc: 2 | ncall: 22220 | eff(%): 20.563 | loglstar: -inf < -7.485 < inf | logz: -16.798 +/- 0.129 | dlogz: 1.211 > 0.010]: </pre>
4672it [00:08, 480.71it/s, batch: 0 | bound: 7 | nc: 2 | ncall: 22220 | eff(%): 20.563 | loglstar: -inf < -7.485 < inf | logz: -16.798 +/- 0.129 | dlogz: 1.211 > 0.010]: end{sphinxVerbatim}

4793it [00:09, 433.70it/s, batch: 0 | bound: 8 | nc: 1 | ncall: 22511 | eff(%): 20.829 | loglstar: -inf < -7.294 < inf | logz: -16.590 +/- 0.129 | dlogz: 0.917 > 0.010]: </pre>
4793it [00:09, 433.70it/s, batch: 0 | bound: 8 | nc: 1 | ncall: 22511 | eff(%): 20.829 | loglstar: -inf < -7.294 < inf | logz: -16.590 +/- 0.129 | dlogz: 0.917 > 0.010]: end{sphinxVerbatim}

4940it [00:09, 573.21it/s, batch: 0 | bound: 8 | nc: 5 | ncall: 22688 | eff(%): 21.304 | loglstar: -inf < -7.122 < inf | logz: -16.400 +/- 0.129 | dlogz: 0.656 > 0.010]: </pre>
4940it [00:09, 573.21it/s, batch: 0 | bound: 8 | nc: 5 | ncall: 22688 | eff(%): 21.304 | loglstar: -inf < -7.122 < inf | logz: -16.400 +/- 0.129 | dlogz: 0.656 > 0.010]: end{sphinxVerbatim}

5057it [00:09, 669.38it/s, batch: 0 | bound: 8 | nc: 2 | ncall: 22887 | eff(%): 21.623 | loglstar: -inf < -7.019 < inf | logz: -16.285 +/- 0.129 | dlogz: 0.503 > 0.010]: </pre>
5057it [00:09, 669.38it/s, batch: 0 | bound: 8 | nc: 2 | ncall: 22887 | eff(%): 21.623 | loglstar: -inf < -7.019 < inf | logz: -16.285 +/- 0.129 | dlogz: 0.503 > 0.010]: end{sphinxVerbatim}

5185it [00:09, 780.90it/s, batch: 0 | bound: 8 | nc: 3 | ncall: 23173 | eff(%): 21.903 | loglstar: -inf < -6.926 < inf | logz: -16.188 +/- 0.129 | dlogz: 0.378 > 0.010]: </pre>
5185it [00:09, 780.90it/s, batch: 0 | bound: 8 | nc: 3 | ncall: 23173 | eff(%): 21.903 | loglstar: -inf < -6.926 < inf | logz: -16.188 +/- 0.129 | dlogz: 0.378 > 0.010]: end{sphinxVerbatim}

5293it [00:09, 544.92it/s, batch: 0 | bound: 9 | nc: 1 | ncall: 23336 | eff(%): 22.206 | loglstar: -inf < -6.872 < inf | logz: -16.123 +/- 0.129 | dlogz: 0.298 > 0.010]: </pre>
5293it [00:09, 544.92it/s, batch: 0 | bound: 9 | nc: 1 | ncall: 23336 | eff(%): 22.206 | loglstar: -inf < -6.872 < inf | logz: -16.123 +/- 0.129 | dlogz: 0.298 > 0.010]: end{sphinxVerbatim}

5431it [00:10, 680.29it/s, batch: 0 | bound: 9 | nc: 1 | ncall: 23514 | eff(%): 22.616 | loglstar: -inf < -6.815 < inf | logz: -16.060 +/- 0.129 | dlogz: 0.221 > 0.010]: </pre>
5431it [00:10, 680.29it/s, batch: 0 | bound: 9 | nc: 1 | ncall: 23514 | eff(%): 22.616 | loglstar: -inf < -6.815 < inf | logz: -16.060 +/- 0.129 | dlogz: 0.221 > 0.010]: end{sphinxVerbatim}

5555it [00:10, 784.11it/s, batch: 0 | bound: 9 | nc: 3 | ncall: 23727 | eff(%): 22.929 | loglstar: -inf < -6.772 < inf | logz: -16.016 +/- 0.129 | dlogz: 0.169 > 0.010]: </pre>
5555it [00:10, 784.11it/s, batch: 0 | bound: 9 | nc: 3 | ncall: 23727 | eff(%): 22.929 | loglstar: -inf < -6.772 < inf | logz: -16.016 +/- 0.129 | dlogz: 0.169 > 0.010]: end{sphinxVerbatim}

5674it [00:10, 870.05it/s, batch: 0 | bound: 9 | nc: 1 | ncall: 23980 | eff(%): 23.178 | loglstar: -inf < -6.737 < inf | logz: -15.982 +/- 0.129 | dlogz: 0.132 > 0.010]: </pre>
5674it [00:10, 870.05it/s, batch: 0 | bound: 9 | nc: 1 | ncall: 23980 | eff(%): 23.178 | loglstar: -inf < -6.737 < inf | logz: -15.982 +/- 0.129 | dlogz: 0.132 > 0.010]: end{sphinxVerbatim}

5785it [00:10, 688.75it/s, batch: 0 | bound: 10 | nc: 1 | ncall: 24134 | eff(%): 23.484 | loglstar: -inf < -6.712 < inf | logz: -15.958 +/- 0.129 | dlogz: 0.104 > 0.010]: </pre>
5785it [00:10, 688.75it/s, batch: 0 | bound: 10 | nc: 1 | ncall: 24134 | eff(%): 23.484 | loglstar: -inf < -6.712 < inf | logz: -15.958 +/- 0.129 | dlogz: 0.104 > 0.010]: end{sphinxVerbatim}

5929it [00:10, 837.45it/s, batch: 0 | bound: 10 | nc: 1 | ncall: 24349 | eff(%): 23.860 | loglstar: -inf < -6.687 < inf | logz: -15.933 +/- 0.129 | dlogz: 0.078 > 0.010]: </pre>
5929it [00:10, 837.45it/s, batch: 0 | bound: 10 | nc: 1 | ncall: 24349 | eff(%): 23.860 | loglstar: -inf < -6.687 < inf | logz: -15.933 +/- 0.129 | dlogz: 0.078 > 0.010]: end{sphinxVerbatim}

6036it [00:10, 757.10it/s, batch: 0 | bound: 10 | nc: 1 | ncall: 24538 | eff(%): 24.107 | loglstar: -inf < -6.672 < inf | logz: -15.919 +/- 0.129 | dlogz: 0.062 > 0.010]: </pre>
6036it [00:10, 757.10it/s, batch: 0 | bound: 10 | nc: 1 | ncall: 24538 | eff(%): 24.107 | loglstar: -inf < -6.672 < inf | logz: -15.919 +/- 0.129 | dlogz: 0.062 > 0.010]: end{sphinxVerbatim}

6136it [00:11, 601.03it/s, batch: 0 | bound: 11 | nc: 1 | ncall: 24764 | eff(%): 24.288 | loglstar: -inf < -6.661 < inf | logz: -15.908 +/- 0.129 | dlogz: 0.051 > 0.010]: </pre>
6136it [00:11, 601.03it/s, batch: 0 | bound: 11 | nc: 1 | ncall: 24764 | eff(%): 24.288 | loglstar: -inf < -6.661 < inf | logz: -15.908 +/- 0.129 | dlogz: 0.051 > 0.010]: end{sphinxVerbatim}

6281it [00:11, 756.44it/s, batch: 0 | bound: 11 | nc: 1 | ncall: 24953 | eff(%): 24.677 | loglstar: -inf < -6.646 < inf | logz: -15.896 +/- 0.129 | dlogz: 0.038 > 0.010]: </pre>
6281it [00:11, 756.44it/s, batch: 0 | bound: 11 | nc: 1 | ncall: 24953 | eff(%): 24.677 | loglstar: -inf < -6.646 < inf | logz: -15.896 +/- 0.129 | dlogz: 0.038 > 0.010]: end{sphinxVerbatim}

6440it [00:11, 929.33it/s, batch: 0 | bound: 11 | nc: 1 | ncall: 25225 | eff(%): 25.034 | loglstar: -inf < -6.635 < inf | logz: -15.886 +/- 0.129 | dlogz: 0.027 > 0.010]: </pre>
6440it [00:11, 929.33it/s, batch: 0 | bound: 11 | nc: 1 | ncall: 25225 | eff(%): 25.034 | loglstar: -inf < -6.635 < inf | logz: -15.886 +/- 0.129 | dlogz: 0.027 > 0.010]: end{sphinxVerbatim}

6556it [00:11, 943.56it/s, batch: 0 | bound: 11 | nc: 1 | ncall: 25481 | eff(%): 25.234 | loglstar: -inf < -6.629 < inf | logz: -15.880 +/- 0.129 | dlogz: 0.022 > 0.010]: </pre>
6556it [00:11, 943.56it/s, batch: 0 | bound: 11 | nc: 1 | ncall: 25481 | eff(%): 25.234 | loglstar: -inf < -6.629 < inf | logz: -15.880 +/- 0.129 | dlogz: 0.022 > 0.010]: end{sphinxVerbatim}

6667it [00:11, 611.02it/s, batch: 0 | bound: 12 | nc: 1 | ncall: 25640 | eff(%): 25.505 | loglstar: -inf < -6.625 < inf | logz: -15.876 +/- 0.129 | dlogz: 0.017 > 0.010]: </pre>
6667it [00:11, 611.02it/s, batch: 0 | bound: 12 | nc: 1 | ncall: 25640 | eff(%): 25.505 | loglstar: -inf < -6.625 < inf | logz: -15.876 +/- 0.129 | dlogz: 0.017 > 0.010]: end{sphinxVerbatim}

6805it [00:11, 745.15it/s, batch: 0 | bound: 12 | nc: 3 | ncall: 25863 | eff(%): 25.813 | loglstar: -inf < -6.621 < inf | logz: -15.872 +/- 0.129 | dlogz: 0.013 > 0.010]: </pre>
6805it [00:11, 745.15it/s, batch: 0 | bound: 12 | nc: 3 | ncall: 25863 | eff(%): 25.813 | loglstar: -inf < -6.621 < inf | logz: -15.872 +/- 0.129 | dlogz: 0.013 > 0.010]: end{sphinxVerbatim}

6918it [00:11, 820.26it/s, batch: 0 | bound: 12 | nc: 4 | ncall: 26083 | eff(%): 26.024 | loglstar: -inf < -6.618 < inf | logz: -15.869 +/- 0.129 | dlogz: 0.010 > 0.010]: </pre>
6918it [00:11, 820.26it/s, batch: 0 | bound: 12 | nc: 4 | ncall: 26083 | eff(%): 26.024 | loglstar: -inf < -6.618 < inf | logz: -15.869 +/- 0.129 | dlogz: 0.010 > 0.010]: end{sphinxVerbatim}

7157it [00:12, 1167.91it/s, batch: 0 | bound: 12 | nc: 1 | ncall: 26370 | eff(%): 26.855 | loglstar: -inf < -6.613 < inf | logz: -15.864 +/- 0.129 | dlogz: 0.006 > 0.010]: </pre>
7157it [00:12, 1167.91it/s, batch: 0 | bound: 12 | nc: 1 | ncall: 26370 | eff(%): 26.855 | loglstar: -inf < -6.613 < inf | logz: -15.864 +/- 0.129 | dlogz: 0.006 > 0.010]: end{sphinxVerbatim}


WARNING DeprecationWarning: This an old stopping function that will be removed in future releases

7438it [00:13, 433.94it/s, batch: 1 | bound: 0 | nc: 1 | ncall: 26651 | eff(%): 27.909 | loglstar: -8.346 < -7.850 < -7.113 | logz: -15.859 +/- 0.132 | stop: 1.406]: </pre>
7438it [00:13, 433.94it/s, batch: 1 | bound: 0 | nc: 1 | ncall: 26651 | eff(%): 27.909 | loglstar: -8.346 < -7.850 < -7.113 | logz: -15.859 +/- 0.132 | stop: 1.406]: end{sphinxVerbatim}

7547it [00:13, 489.69it/s, batch: 1 | bound: 2 | nc: 1 | ncall: 26775 | eff(%): 27.637 | loglstar: -8.346 < -8.047 < -7.113 | logz: -15.859 +/- 0.132 | stop: 1.406]: </pre>
7547it [00:13, 489.69it/s, batch: 1 | bound: 2 | nc: 1 | ncall: 26775 | eff(%): 27.637 | loglstar: -8.346 < -8.047 < -7.113 | logz: -15.859 +/- 0.132 | stop: 1.406]: end{sphinxVerbatim}

7655it [00:13, 552.73it/s, batch: 1 | bound: 2 | nc: 1 | ncall: 26956 | eff(%): 27.848 | loglstar: -8.346 < -7.750 < -7.113 | logz: -15.859 +/- 0.132 | stop: 1.406]: </pre>
7655it [00:13, 552.73it/s, batch: 1 | bound: 2 | nc: 1 | ncall: 26956 | eff(%): 27.848 | loglstar: -8.346 < -7.750 < -7.113 | logz: -15.859 +/- 0.132 | stop: 1.406]: end{sphinxVerbatim}

7762it [00:13, 587.83it/s, batch: 1 | bound: 2 | nc: 4 | ncall: 27176 | eff(%): 28.013 | loglstar: -8.346 < -7.550 < -7.113 | logz: -15.859 +/- 0.132 | stop: 1.406]: </pre>
7762it [00:13, 587.83it/s, batch: 1 | bound: 2 | nc: 4 | ncall: 27176 | eff(%): 28.013 | loglstar: -8.346 < -7.550 < -7.113 | logz: -15.859 +/- 0.132 | stop: 1.406]: end{sphinxVerbatim}

7859it [00:13, 571.61it/s, batch: 1 | bound: 2 | nc: 4 | ncall: 27386 | eff(%): 28.149 | loglstar: -8.346 < -7.370 < -7.113 | logz: -15.859 +/- 0.132 | stop: 1.406]: </pre>
7859it [00:13, 571.61it/s, batch: 1 | bound: 2 | nc: 4 | ncall: 27386 | eff(%): 28.149 | loglstar: -8.346 < -7.370 < -7.113 | logz: -15.859 +/- 0.132 | stop: 1.406]: end{sphinxVerbatim}

7943it [00:14, 427.95it/s, batch: 1 | bound: 3 | nc: 3 | ncall: 27500 | eff(%): 28.334 | loglstar: -8.346 < -7.246 < -7.113 | logz: -15.859 +/- 0.132 | stop: 1.406]: </pre>
7943it [00:14, 427.95it/s, batch: 1 | bound: 3 | nc: 3 | ncall: 27500 | eff(%): 28.334 | loglstar: -8.346 < -7.246 < -7.113 | logz: -15.859 +/- 0.132 | stop: 1.406]: end{sphinxVerbatim}

8217it [00:14, 750.73it/s, batch: 1 | bound: 3 | nc: 1 | ncall: 27850 | eff(%): 29.115 | loglstar: -8.346 < -6.958 < -7.113 | logz: -15.859 +/- 0.132 | stop: 1.406]: </pre>
8217it [00:14, 750.73it/s, batch: 1 | bound: 3 | nc: 1 | ncall: 27850 | eff(%): 29.115 | loglstar: -8.346 < -6.958 < -7.113 | logz: -15.859 +/- 0.132 | stop: 1.406]: end{sphinxVerbatim}


WARNING DeprecationWarning: This an old stopping function that will be removed in future releases

8568it [00:15, 421.98it/s, batch: 2 | bound: 0 | nc: 1 | ncall: 28223 | eff(%): 30.358 | loglstar: -8.865 < -6.918 < -8.345 | logz: -15.871 +/- 0.109 | stop: 1.147]: </pre>
8568it [00:15, 421.98it/s, batch: 2 | bound: 0 | nc: 1 | ncall: 28223 | eff(%): 30.358 | loglstar: -8.865 < -6.918 < -8.345 | logz: -15.871 +/- 0.109 | stop: 1.147]: end{sphinxVerbatim}

8787it [00:15, 557.24it/s, batch: 2 | bound: 2 | nc: 1 | ncall: 28479 | eff(%): 30.365 | loglstar: -8.865 < -7.967 < -8.345 | logz: -15.871 +/- 0.109 | stop: 1.147]: </pre>
8787it [00:15, 557.24it/s, batch: 2 | bound: 2 | nc: 1 | ncall: 28479 | eff(%): 30.365 | loglstar: -8.865 < -7.967 < -8.345 | logz: -15.871 +/- 0.109 | stop: 1.147]: end{sphinxVerbatim}


WARNING DeprecationWarning: This an old stopping function that will be removed in future releases

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22:19:19 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 +/- 0.16) x 10^-1	1 / (cm2 keV s)
demo.spectrum.main.Sin.f	(9.99 +/- 0.05) x 10^-2	rad / keV

Values of -log(posterior) at the minimum:

	-log(posterior)
demo	-6.59844
total	-6.59844

Values of statistical measures:

	statistical measures
AIC	17.902762
BIC	19.188344
DIC	16.982383
PDIC	1.892672
log(Z)	-6.889652

[8]:

../_images/notebooks_sampler_docs_12_104.png

../_images/notebooks_sampler_docs_12_105.png

../_images/notebooks_sampler_docs_12_106.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()

22:19:21 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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22:19:39 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: 36

Scale Factor: 1.160638

Mean Integrated Autocorrelation Time: 3.2

Effective Sample Size: 3909.9

Number of Log Probability Evaluations: 66005

Effective Samples per Log Probability Evaluation: 0.059236

None

Maximum a posteriori probability (MAP) point:

	result	unit
parameter
demo.spectrum.main.Sin.K	(9.91 +/- 0.16) x 10^-1	1 / (cm2 keV s)
demo.spectrum.main.Sin.f	(9.99 +/- 0.05) x 10^-2	rad / keV

Values of -log(posterior) at the minimum:

	-log(posterior)
demo	-6.598622
total	-6.598622

Values of statistical measures:

	statistical measures
AIC	17.903126
BIC	19.188708
DIC	17.120586
PDIC	1.961771

[9]:

../_images/notebooks_sampler_docs_14_156.png

../_images/notebooks_sampler_docs_14_157.png

../_images/notebooks_sampler_docs_14_158.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()

22:19:40 INFO      sampler set to ultranest                                                bayesian_analysis.py:202

[ultranest] Sampling 400 live points from prior ...

Z=-inf(0.00%) | Like=-9686.44..-35.24 [-9686.4396..-3209.8402] | it/evals=0/401 eff=0.0000% N=400

Z=-6499.0(0.00%) | Like=-6479.79..-35.24 [-9686.4396..-3209.8402] | it/evals=40/442 eff=95.2381% N=400

Z=-5416.0(0.00%) | Like=-5405.93..-35.24 [-9686.4396..-3209.8402] | it/evals=79/489 eff=88.7640% N=400

Z=-5412.1(0.00%) | Like=-5363.98..-35.24 [-9686.4396..-3209.8402] | it/evals=80/490 eff=88.8889% N=400

Z=-5169.9(0.00%) | Like=-5161.98..-35.24 [-9686.4396..-3209.8402] | it/evals=90/502 eff=88.2353% N=400

Z=-4680.7(0.00%) | Like=-4662.57..-29.92 [-9686.4396..-3209.8402] | it/evals=120/533 eff=90.2256% N=400

Z=-4107.3(0.00%) | Like=-4099.40..-29.92 [-9686.4396..-3209.8402] | it/evals=160/588 eff=85.1064% N=400

Z=-3874.4(0.00%) | Like=-3861.87..-29.92 [-9686.4396..-3209.8402] | it/evals=180/617 eff=82.9493% N=400

Z=-3721.5(0.00%) | Like=-3702.89..-29.92 [-9686.4396..-3209.8402] | it/evals=200/642 eff=82.6446% N=400

Z=-3437.0(0.00%) | Like=-3417.06..-14.10 [-9686.4396..-3209.8402] | it/evals=240/699 eff=80.2676% N=400

Z=-3239.0(0.00%) | Like=-3231.59..-14.10 [-9686.4396..-3209.8402] | it/evals=270/745 eff=78.2609% N=400

Z=-3201.6(0.00%) | Like=-3189.07..-14.10 [-3198.8495..-2121.9750] | it/evals=280/761 eff=77.5623% N=400

Z=-2998.7(0.00%) | Like=-2989.38..-14.10 [-3198.8495..-2121.9750] | it/evals=320/831 eff=74.2459% N=400

Z=-2811.6(0.00%) | Like=-2804.86..-14.10 [-3198.8495..-2121.9750] | it/evals=360/925 eff=68.5714% N=400

Z=-2672.8(0.00%) | Like=-2664.04..-14.10 [-3198.8495..-2121.9750] | it/evals=395/996 eff=66.2752% N=400

Z=-2657.0(0.00%) | Like=-2647.70..-14.10 [-3198.8495..-2121.9750] | it/evals=400/1008 eff=65.7895% N=400

Z=-2518.7(0.00%) | Like=-2505.61..-14.10 [-3198.8495..-2121.9750] | it/evals=440/1109 eff=62.0592% N=400

Z=-2471.2(0.00%) | Like=-2463.31..-14.10 [-3198.8495..-2121.9750] | it/evals=450/1136 eff=61.1413% N=400

Z=-2388.4(0.00%) | Like=-2381.42..-14.10 [-3198.8495..-2121.9750] | it/evals=475/1198 eff=59.5238% N=400

Z=-2376.4(0.00%) | Like=-2354.43..-14.10 [-3198.8495..-2121.9750] | it/evals=480/1217 eff=58.7515% N=400

Z=-2239.2(0.00%) | Like=-2231.51..-14.10 [-3198.8495..-2121.9750] | it/evals=520/1306 eff=57.3951% N=400

Z=-2161.1(0.00%) | Like=-2149.53..-14.10 [-3198.8495..-2121.9750] | it/evals=556/1400 eff=55.6000% N=400

Z=-2143.9(0.00%) | Like=-2135.99..-14.10 [-3198.8495..-2121.9750] | it/evals=560/1408 eff=55.5556% N=400

Z=-2062.1(0.00%) | Like=-2055.04..-14.10 [-2121.2236..-1151.5067] | it/evals=600/1525 eff=53.3333% N=400

Z=-1994.7(0.00%) | Like=-1986.10..-14.10 [-2121.2236..-1151.5067] | it/evals=630/1633 eff=51.0949% N=400

Z=-1962.1(0.00%) | Like=-1951.90..-14.10 [-2121.2236..-1151.5067] | it/evals=640/1656 eff=50.9554% N=400

Z=-1935.2(0.00%) | Like=-1928.68..-14.10 [-2121.2236..-1151.5067] | it/evals=680/1735 eff=50.9363% N=400

Z=-1731.4(0.00%) | Like=-1720.45..-14.10 [-2121.2236..-1151.5067] | it/evals=720/1848 eff=49.7238% N=400

Z=-1508.3(0.00%) | Like=-1499.83..-14.10 [-2121.2236..-1151.5067] | it/evals=760/1916 eff=50.1319% N=400

Z=-1371.3(0.00%) | Like=-1357.55..-14.10 [-2121.2236..-1151.5067] | it/evals=800/1976 eff=50.7614% N=400

Z=-1331.4(0.00%) | Like=-1321.95..-14.10 [-2121.2236..-1151.5067] | it/evals=810/1990 eff=50.9434% N=400

Z=-1229.7(0.00%) | Like=-1220.04..-14.10 [-2121.2236..-1151.5067] | it/evals=840/2043 eff=51.1260% N=400

Z=-1059.6(0.00%) | Like=-1050.23..-14.10 [-1149.0606..-495.9028] | it/evals=880/2110 eff=51.4620% N=400

Z=-987.1(0.00%) | Like=-976.84..-14.10 [-1149.0606..-495.9028] | it/evals=900/2145 eff=51.5759% N=400

Z=-922.6(0.00%) | Like=-911.92..-14.10 [-1149.0606..-495.9028] | it/evals=920/2175 eff=51.8310% N=400

Z=-816.2(0.00%) | Like=-800.93..-14.10 [-1149.0606..-495.9028] | it/evals=960/2242 eff=52.1173% N=400

Z=-746.5(0.00%) | Like=-732.79..-14.10 [-1149.0606..-495.9028] | it/evals=990/2294 eff=52.2703% N=400

Z=-723.9(0.00%) | Like=-712.32..-14.10 [-1149.0606..-495.9028] | it/evals=1000/2307 eff=52.4384% N=400

Z=-651.9(0.00%) | Like=-642.68..-6.74 [-1149.0606..-495.9028] | it/evals=1040/2362 eff=53.0071% N=400

Z=-581.5(0.00%) | Like=-566.71..-6.74 [-1149.0606..-495.9028] | it/evals=1080/2431 eff=53.1758% N=400

Z=-513.5(0.00%) | Like=-504.23..-6.74 [-1149.0606..-495.9028] | it/evals=1120/2478 eff=53.8980% N=400

Z=-464.1(0.00%) | Like=-455.43..-6.74 [-495.8124..-274.9311] | it/evals=1160/2535 eff=54.3326% N=400

Z=-451.7(0.00%) | Like=-442.04..-6.74 [-495.8124..-274.9311] | it/evals=1170/2554 eff=54.3175% N=400

Z=-427.9(0.00%) | Like=-419.28..-6.74 [-495.8124..-274.9311] | it/evals=1200/2592 eff=54.7445% N=400

Z=-393.3(0.00%) | Like=-384.58..-6.74 [-495.8124..-274.9311] | it/evals=1240/2645 eff=55.2339% N=400

Z=-381.6(0.00%) | Like=-373.09..-6.74 [-495.8124..-274.9311] | it/evals=1260/2675 eff=55.3846% N=400

Z=-360.2(0.00%) | Like=-350.55..-6.74 [-495.8124..-274.9311] | it/evals=1280/2703 eff=55.5797% N=400

Z=-335.7(0.00%) | Like=-325.44..-6.74 [-495.8124..-274.9311] | it/evals=1320/2758 eff=55.9796% N=400

Z=-315.8(0.00%) | Like=-307.52..-6.74 [-495.8124..-274.9311] | it/evals=1350/2801 eff=56.2266% N=400

Z=-306.6(0.00%) | Like=-296.88..-6.74 [-495.8124..-274.9311] | it/evals=1360/2813 eff=56.3614% N=400

Z=-283.2(0.00%) | Like=-274.55..-6.74 [-274.6545..-160.8274] | it/evals=1400/2869 eff=56.7031% N=400

Z=-258.5(0.00%) | Like=-247.55..-6.74 [-274.6545..-160.8274] | it/evals=1440/2925 eff=57.0297% N=400

Z=-238.7(0.00%) | Like=-227.65..-6.74 [-274.6545..-160.8274] | it/evals=1480/2977 eff=57.4311% N=400

Z=-220.4(0.00%) | Like=-212.22..-6.74 [-274.6545..-160.8274] | it/evals=1520/3032 eff=57.7508% N=400

Z=-215.7(0.00%) | Like=-206.39..-6.74 [-274.6545..-160.8274] | it/evals=1530/3047 eff=57.8013% N=400

Z=-205.0(0.00%) | Like=-195.94..-6.74 [-274.6545..-160.8274] | it/evals=1560/3083 eff=58.1439% N=400

Z=-192.3(0.00%) | Like=-183.66..-6.74 [-274.6545..-160.8274] | it/evals=1600/3138 eff=58.4368% N=400

Z=-186.6(0.00%) | Like=-176.80..-6.74 [-274.6545..-160.8274] | it/evals=1620/3168 eff=58.5260% N=400

Z=-179.7(0.00%) | Like=-170.88..-6.74 [-274.6545..-160.8274] | it/evals=1640/3192 eff=58.7393% N=400

Z=-168.0(0.00%) | Like=-159.27..-6.74 [-160.7165..-88.0547] | it/evals=1680/3243 eff=59.0925% N=400

Z=-158.9(0.00%) | Like=-149.99..-6.74 [-160.7165..-88.0547] | it/evals=1710/3277 eff=59.4369% N=400

Z=-155.0(0.00%) | Like=-145.76..-6.74 [-160.7165..-88.0547] | it/evals=1720/3290 eff=59.5156% N=400

Z=-140.7(0.00%) | Like=-131.34..-6.74 [-160.7165..-88.0547] | it/evals=1760/3343 eff=59.8029% N=400

Z=-129.9(0.00%) | Like=-120.60..-6.74 [-160.7165..-88.0547] | it/evals=1800/3395 eff=60.1002% N=400

Z=-119.6(0.00%) | Like=-110.46..-6.74 [-160.7165..-88.0547] | it/evals=1840/3448 eff=60.3675% N=400

Z=-111.2(0.00%) | Like=-102.30..-6.74 [-160.7165..-88.0547] | it/evals=1880/3501 eff=60.6256% N=400

Z=-109.5(0.00%) | Like=-99.53..-6.74 [-160.7165..-88.0547] | it/evals=1890/3515 eff=60.6742% N=400

Z=-101.8(0.00%) | Like=-92.87..-6.74 [-160.7165..-88.0547] | it/evals=1920/3552 eff=60.9137% N=400

Z=-94.7(0.00%) | Like=-85.74..-6.74 [-88.0360..-48.8260] | it/evals=1960/3603 eff=61.1926% N=400

Z=-91.0(0.00%) | Like=-81.99..-6.74 [-88.0360..-48.8260] | it/evals=1980/3627 eff=61.3573% N=400

Z=-88.2(0.00%) | Like=-79.07..-6.74 [-88.0360..-48.8260] | it/evals=2000/3652 eff=61.5006% N=400

Z=-80.2(0.00%) | Like=-70.43..-6.74 [-88.0360..-48.8260] | it/evals=2040/3702 eff=61.7807% N=400

Z=-75.0(0.00%) | Like=-65.77..-6.74 [-88.0360..-48.8260] | it/evals=2070/3743 eff=61.9204% N=400

Z=-73.9(0.00%) | Like=-65.01..-6.74 [-88.0360..-48.8260] | it/evals=2080/3754 eff=62.0155% N=400

Z=-68.7(0.00%) | Like=-59.46..-6.74 [-88.0360..-48.8260] | it/evals=2120/3809 eff=62.1883% N=400

Z=-63.8(0.00%) | Like=-54.58..-6.74 [-88.0360..-48.8260] | it/evals=2160/3874 eff=62.1762% N=400

Z=-60.1(0.00%) | Like=-50.91..-6.74 [-88.0360..-48.8260] | it/evals=2200/3929 eff=62.3406% N=400

Z=-56.5(0.00%) | Like=-47.26..-6.74 [-48.8194..-28.4626] | it/evals=2240/3985 eff=62.4826% N=400

Z=-55.7(0.00%) | Like=-46.41..-6.74 [-48.8194..-28.4626] | it/evals=2250/4000 eff=62.5000% N=400

Z=-52.7(0.00%) | Like=-43.27..-6.74 [-48.8194..-28.4626] | it/evals=2280/4034 eff=62.7408% N=400

Z=-49.2(0.00%) | Like=-40.04..-6.74 [-48.8194..-28.4626] | it/evals=2320/4085 eff=62.9579% N=400

Z=-47.6(0.00%) | Like=-38.11..-6.74 [-48.8194..-28.4626] | it/evals=2340/4116 eff=62.9709% N=400

Z=-46.0(0.00%) | Like=-36.87..-6.74 [-48.8194..-28.4626] | it/evals=2360/4144 eff=63.0342% N=400

Z=-43.3(0.00%) | Like=-34.12..-6.74 [-48.8194..-28.4626] | it/evals=2400/4196 eff=63.2244% N=400

Z=-41.3(0.00%) | Like=-32.02..-6.74 [-48.8194..-28.4626] | it/evals=2430/4241 eff=63.2648% N=400

Z=-40.7(0.00%) | Like=-31.68..-6.74 [-48.8194..-28.4626] | it/evals=2440/4251 eff=63.3602% N=400

Z=-38.7(0.00%) | Like=-29.32..-6.65 [-48.8194..-28.4626] | it/evals=2480/4308 eff=63.4596% N=400

Z=-36.6(0.00%) | Like=-27.35..-6.65 [-28.4235..-18.4605] | it/evals=2520/4369 eff=63.4921% N=400

Z=-34.5(0.00%) | Like=-25.03..-6.65 [-28.4235..-18.4605] | it/evals=2560/4431 eff=63.5078% N=400

Z=-32.7(0.00%) | Like=-23.17..-6.65 [-28.4235..-18.4605] | it/evals=2600/4485 eff=63.6475% N=400

Z=-32.1(0.00%) | Like=-22.71..-6.65 [-28.4235..-18.4605] | it/evals=2610/4507 eff=63.5500% N=400

Z=-30.8(0.00%) | Like=-21.44..-6.65 [-28.4235..-18.4605] | it/evals=2640/4543 eff=63.7219% N=400

Z=-29.5(0.00%) | Like=-20.23..-6.65 [-28.4235..-18.4605] | it/evals=2680/4604 eff=63.7488% N=400

Z=-28.9(0.00%) | Like=-19.68..-6.65 [-28.4235..-18.4605] | it/evals=2700/4637 eff=63.7243% N=400

Z=-28.3(0.00%) | Like=-19.14..-6.65 [-28.4235..-18.4605] | it/evals=2720/4657 eff=63.8948% N=400

Z=-27.3(0.00%) | Like=-18.07..-6.65 [-18.4230..-14.4562] | it/evals=2760/4702 eff=64.1562% N=400

Z=-26.6(0.00%) | Like=-17.32..-6.65 [-18.4230..-14.4562] | it/evals=2790/4748 eff=64.1674% N=400

Z=-26.3(0.00%) | Like=-16.85..-6.65 [-18.4230..-14.4562] | it/evals=2800/4762 eff=64.1907% N=400

Z=-25.3(0.01%) | Like=-16.00..-6.65 [-18.4230..-14.4562] | it/evals=2840/4809 eff=64.4137% N=400

Z=-24.4(0.02%) | Like=-15.07..-6.65 [-18.4230..-14.4562] | it/evals=2880/4873 eff=64.3863% N=400

Z=-23.6(0.05%) | Like=-14.37..-6.65 [-14.4184..-13.9757] | it/evals=2920/4922 eff=64.5732% N=400

Z=-23.0(0.09%) | Like=-13.77..-6.65 [-13.7655..-13.7651]*| it/evals=2960/4977 eff=64.6712% N=400

Z=-22.8(0.11%) | Like=-13.57..-6.65 [-13.6204..-13.5711] | it/evals=2970/4990 eff=64.7059% N=400

Z=-22.4(0.17%) | Like=-13.06..-6.65 [-13.0593..-13.0500]*| it/evals=3000/5025 eff=64.8649% N=400

Z=-21.8(0.32%) | Like=-12.43..-6.65 [-12.4301..-12.4266]*| it/evals=3040/5077 eff=64.9989% N=400

Z=-21.5(0.42%) | Like=-12.22..-6.65 [-12.2217..-12.2213]*| it/evals=3060/5112 eff=64.9406% N=400

Z=-21.3(0.53%) | Like=-11.95..-6.65 [-11.9651..-11.9492] | it/evals=3080/5135 eff=65.0475% N=400

Z=-20.8(0.86%) | Like=-11.49..-6.65 [-11.4997..-11.4884] | it/evals=3120/5183 eff=65.2310% N=400

Z=-20.5(1.18%) | Like=-11.17..-6.63 [-11.1658..-11.1562]*| it/evals=3150/5222 eff=65.3256% N=400

Z=-20.4(1.31%) | Like=-11.04..-6.63 [-11.0442..-11.0422]*| it/evals=3160/5232 eff=65.3974% N=400

Z=-20.0(1.94%) | Like=-10.67..-6.63 [-10.6703..-10.6682]*| it/evals=3200/5279 eff=65.5872% N=400

Z=-19.6(2.77%) | Like=-10.26..-6.63 [-10.2578..-10.2452] | it/evals=3240/5327 eff=65.7601% N=400

Z=-19.3(3.87%) | Like=-9.82..-6.63 [-9.8347..-9.8185] | it/evals=3280/5382 eff=65.8370% N=400

Z=-19.0(5.26%) | Like=-9.55..-6.63 [-9.5525..-9.5512]*| it/evals=3320/5443 eff=65.8338% N=400

Z=-18.9(5.68%) | Like=-9.49..-6.63 [-9.4924..-9.4920]*| it/evals=3330/5454 eff=65.8884% N=400

Z=-18.7(7.06%) | Like=-9.30..-6.63 [-9.3151..-9.3049] | it/evals=3360/5487 eff=66.0507% N=400

Z=-18.4(9.10%) | Like=-9.05..-6.63 [-9.0473..-9.0322] | it/evals=3400/5540 eff=66.1479% N=400

Z=-18.3(10.32%) | Like=-8.90..-6.63 [-8.8996..-8.8970]*| it/evals=3420/5570 eff=66.1509% N=400

Z=-18.2(11.64%) | Like=-8.79..-6.63 [-8.8046..-8.7945] | it/evals=3440/5596 eff=66.2048% N=400

Z=-18.2(11.88%) | Like=-8.75..-6.63 [-8.7549..-8.7391] | it/evals=3446/5607 eff=66.1801% N=400

Z=-18.0(14.11%) | Like=-8.58..-6.61 [-8.5750..-8.5747]*| it/evals=3480/5663 eff=66.1220% N=400

Z=-17.8(16.14%) | Like=-8.43..-6.61 [-8.4316..-8.4249]*| it/evals=3510/5710 eff=66.1017% N=400

Z=-17.8(16.95%) | Like=-8.40..-6.61 [-8.4041..-8.3992]*| it/evals=3520/5724 eff=66.1157% N=400

Z=-17.6(20.12%) | Like=-8.25..-6.61 [-8.2492..-8.2477]*| it/evals=3560/5775 eff=66.2326% N=400

Z=-17.6(20.20%) | Like=-8.25..-6.61 [-8.2477..-8.2467]*| it/evals=3561/5776 eff=66.2388% N=400

Z=-17.5(23.33%) | Like=-8.11..-6.61 [-8.1083..-8.1057]*| it/evals=3600/5835 eff=66.2374% N=400

Z=-17.3(26.53%) | Like=-7.99..-6.61 [-7.9892..-7.9861]*| it/evals=3640/5889 eff=66.3144% N=400

Z=-17.2(29.84%) | Like=-7.83..-6.61 [-7.8296..-7.8294]*| it/evals=3680/5943 eff=66.3900% N=400

Z=-17.2(30.78%) | Like=-7.81..-6.61 [-7.8121..-7.8086]*| it/evals=3690/5960 eff=66.3669% N=400

Z=-17.1(33.39%) | Like=-7.74..-6.61 [-7.7368..-7.7321]*| it/evals=3720/5993 eff=66.5117% N=400

Z=-17.0(36.81%) | Like=-7.61..-6.61 [-7.6118..-7.6098]*| it/evals=3760/6041 eff=66.6548% N=400

Z=-16.9(38.67%) | Like=-7.55..-6.61 [-7.5541..-7.5501]*| it/evals=3780/6074 eff=66.6197% N=400

Z=-16.9(40.50%) | Like=-7.50..-6.61 [-7.5000..-7.4996]*| it/evals=3800/6097 eff=66.7018% N=400

Z=-16.8(43.96%) | Like=-7.41..-6.61 [-7.4130..-7.4117]*| it/evals=3840/6152 eff=66.7594% N=400

Z=-16.8(46.62%) | Like=-7.36..-6.61 [-7.3563..-7.3562]*| it/evals=3870/6199 eff=66.7356% N=400

Z=-16.7(47.44%) | Like=-7.33..-6.61 [-7.3341..-7.3316]*| it/evals=3880/6211 eff=66.7699% N=400

[ultranest] Explored until L=-7

[ultranest] Likelihood function evaluations: 6243

[ultranest]   logZ = -15.99 +- 0.09775

[ultranest] Effective samples strategy satisfied (ESS = 983.7, need >400)

[ultranest] Posterior uncertainty strategy is satisfied (KL: 0.45+-0.05 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.

22:19:52 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	(9.92 -0.16 +0.15) x 10^-1	1 / (cm2 keV s)
demo.spectrum.main.Sin.f	(9.99 +/- 0.05) x 10^-2	rad / keV

Values of -log(posterior) at the minimum:

	-log(posterior)
demo	-6.602016
total	-6.602016

Values of statistical measures:

	statistical measures
AIC	17.909915
BIC	19.195497
DIC	17.190724
PDIC	1.996892
log(Z)	-6.946315

[10]:

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