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()

18:25:39 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.

         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))

18:25:41 INFO      Using Gaussian statistic (equivalent to chi^2) with the provided errors.            XYLike.py:93

         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

18:25:44 INFO      Mean acceptance fraction: 0.7199                                            emcee_sampler.py:157

18:25:45 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	1.015 -0.014 +0.016	1 / (cm2 keV s)
demo.spectrum.main.Sin.f	(9.96 +/- 0.05) x 10^-2	rad / keV

Values of -log(posterior) at the minimum:

	-log(posterior)
demo	-7.541238
total	-7.541238

Values of statistical measures:

	statistical measures
AIC	19.788359
BIC	21.073941
DIC	19.199965
PDIC	2.057989

[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()

         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)=  -17.055011698864593      +/-  0.14576679544295126
 Total Likelihood Evaluations:         5308
 Sampling finished. Exiting MultiNest

18:25:46 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	1.016 -0.016 +0.014	1 / (cm2 keV s)
demo.spectrum.main.Sin.f	(9.96 -0.05 +0.06) x 10^-2	rad / keV

Values of -log(posterior) at the minimum:

	-log(posterior)
demo	-7.541119
total	-7.541119

Values of statistical measures:

	statistical measures
AIC	19.788120
BIC	21.073702
DIC	19.254705
PDIC	2.085325
log(Z)	-7.406897

         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()

18:25:47 INFO      sampler set to dynesty_nested                                           bayesian_analysis.py:202

0it [00:00, ?it/s]: </pre>
0it [00:00, ?it/s]: end{sphinxVerbatim}

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

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248it [00:00, 2477.52it/s, bound: 0 | nc: 2 | ncall: 727 | eff(%): 34.113 | loglstar: -inf < -2888.638 < inf | logz: -2895.942 +/- 0.135 | dlogz: 2912.926 > 0.409]: end{sphinxVerbatim}

496it [00:00, 1712.77it/s, bound: 0 | nc: 12 | ncall: 1340 | eff(%): 37.015 | loglstar: -inf < -2114.594 < inf | logz: -2121.656 +/- 0.131 | dlogz: 2113.189 > 0.409]: </pre>
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839it [00:00, 1238.56it/s, bound: 0 | nc: 1 | ncall: 3167 | eff(%): 26.492 | loglstar: -inf < -1307.672 < inf | logz: -1316.445 +/- 0.148 | dlogz: 1311.600 > 0.409]: </pre>
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1072it [00:01, 760.11it/s, bound: 0 | nc: 52 | ncall: 6395 | eff(%): 16.763 | loglstar: -inf < -594.720 < inf | logz: -604.034 +/- 0.151 | dlogz: 596.466 > 0.409]: </pre>
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1158it [00:01, 642.84it/s, bound: 0 | nc: 19 | ncall: 7973 | eff(%): 14.524 | loglstar: -inf < -484.434 < inf | logz: -493.231 +/- 0.142 | dlogz: 482.923 > 0.409]: </pre>
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1229it [00:01, 536.71it/s, bound: 0 | nc: 20 | ncall: 9516 | eff(%): 12.915 | loglstar: -inf < -403.189 < inf | logz: -411.390 +/- 0.138 | dlogz: 400.313 > 0.409]: </pre>
1229it [00:01, 536.71it/s, bound: 0 | nc: 20 | ncall: 9516 | eff(%): 12.915 | loglstar: -inf < -403.189 < inf | logz: -411.390 +/- 0.138 | dlogz: 400.313 > 0.409]: end{sphinxVerbatim}

1288it [00:01, 330.89it/s, bound: 0 | nc: 9 | ncall: 11373 | eff(%): 11.325 | loglstar: -inf < -344.816 < inf | logz: -353.552 +/- 0.144 | dlogz: 342.783 > 0.409]: </pre>
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1333it [00:02, 296.95it/s, bound: 0 | nc: 10 | ncall: 12841 | eff(%): 10.381 | loglstar: -inf < -310.465 < inf | logz: -319.094 +/- 0.142 | dlogz: 307.954 > 0.409]: </pre>
1333it [00:02, 296.95it/s, bound: 0 | nc: 10 | ncall: 12841 | eff(%): 10.381 | loglstar: -inf < -310.465 < inf | logz: -319.094 +/- 0.142 | dlogz: 307.954 > 0.409]: end{sphinxVerbatim}

1370it [00:02, 259.15it/s, bound: 1 | nc: 2 | ncall: 13624 | eff(%): 10.056 | loglstar: -inf < -285.176 < inf | logz: -295.021 +/- 0.149 | dlogz: 284.762 > 0.409]: </pre>
1370it [00:02, 259.15it/s, bound: 1 | nc: 2 | ncall: 13624 | eff(%): 10.056 | loglstar: -inf < -285.176 < inf | logz: -295.021 +/- 0.149 | dlogz: 284.762 > 0.409]: end{sphinxVerbatim}

1540it [00:02, 469.94it/s, bound: 1 | nc: 1 | ncall: 13877 | eff(%): 11.097 | loglstar: -inf < -188.996 < inf | logz: -197.711 +/- 0.139 | dlogz: 185.715 > 0.409]: </pre>
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1674it [00:02, 499.43it/s, bound: 2 | nc: 1 | ncall: 14198 | eff(%): 11.790 | loglstar: -inf < -139.864 < inf | logz: -148.660 +/- 0.137 | dlogz: 136.242 > 0.409]: </pre>
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1907it [00:02, 801.85it/s, bound: 2 | nc: 10 | ncall: 14571 | eff(%): 13.088 | loglstar: -inf < -86.836 < inf | logz: -95.912 +/- 0.142 | dlogz: 82.873 > 0.409]: </pre>
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2024it [00:03, 544.94it/s, bound: 3 | nc: 1 | ncall: 14813 | eff(%): 13.664 | loglstar: -inf < -69.373 < inf | logz: -78.616 +/- 0.145 | dlogz: 66.183 > 0.409]: </pre>
2024it [00:03, 544.94it/s, bound: 3 | nc: 1 | ncall: 14813 | eff(%): 13.664 | loglstar: -inf < -69.373 < inf | logz: -78.616 +/- 0.145 | dlogz: 66.183 > 0.409]: end{sphinxVerbatim}

2207it [00:03, 732.31it/s, bound: 3 | nc: 1 | ncall: 15076 | eff(%): 14.639 | loglstar: -inf < -44.847 < inf | logz: -54.172 +/- 0.144 | dlogz: 41.216 > 0.409]: </pre>
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2349it [00:03, 722.60it/s, bound: 4 | nc: 1 | ncall: 15399 | eff(%): 15.254 | loglstar: -inf < -33.846 < inf | logz: -42.945 +/- 0.143 | dlogz: 29.589 > 0.409]: </pre>
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2503it [00:03, 861.59it/s, bound: 4 | nc: 1 | ncall: 15601 | eff(%): 16.044 | loglstar: -inf < -26.366 < inf | logz: -35.354 +/- 0.141 | dlogz: 21.606 > 0.409]: </pre>
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2622it [00:03, 910.83it/s, bound: 4 | nc: 1 | ncall: 15836 | eff(%): 16.557 | loglstar: -inf < -21.896 < inf | logz: -30.957 +/- 0.143 | dlogz: 16.907 > 0.409]: </pre>
2622it [00:03, 910.83it/s, bound: 4 | nc: 1 | ncall: 15836 | eff(%): 16.557 | loglstar: -inf < -21.896 < inf | logz: -30.957 +/- 0.143 | dlogz: 16.907 > 0.409]: end{sphinxVerbatim}

2738it [00:03, 790.53it/s, bound: 5 | nc: 3 | ncall: 16040 | eff(%): 17.070 | loglstar: -inf < -18.245 < inf | logz: -27.322 +/- 0.143 | dlogz: 12.975 > 0.409]: </pre>
2738it [00:03, 790.53it/s, bound: 5 | nc: 3 | ncall: 16040 | eff(%): 17.070 | loglstar: -inf < -18.245 < inf | logz: -27.322 +/- 0.143 | dlogz: 12.975 > 0.409]: end{sphinxVerbatim}

2926it [00:04, 1010.72it/s, bound: 5 | nc: 1 | ncall: 16331 | eff(%): 17.917 | loglstar: -inf < -13.854 < inf | logz: -23.208 +/- 0.144 | dlogz: 8.387 > 0.409]: </pre>
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3051it [00:04, 895.45it/s, bound: 6 | nc: 1 | ncall: 16602 | eff(%): 18.377 | loglstar: -inf < -12.350 < inf | logz: -21.442 +/- 0.143 | dlogz: 6.302 > 0.409]: </pre>
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3253it [00:04, 1133.99it/s, bound: 6 | nc: 1 | ncall: 16881 | eff(%): 19.270 | loglstar: -inf < -10.409 < inf | logz: -19.597 +/- 0.143 | dlogz: 3.977 > 0.409]: </pre>
3253it [00:04, 1133.99it/s, bound: 6 | nc: 1 | ncall: 16881 | eff(%): 19.270 | loglstar: -inf < -10.409 < inf | logz: -19.597 +/- 0.143 | dlogz: 3.977 > 0.409]: end{sphinxVerbatim}

3390it [00:04, 849.89it/s, bound: 7 | nc: 2 | ncall: 17200 | eff(%): 19.709 | loglstar: -inf < -9.665 < inf | logz: -18.779 +/- 0.143 | dlogz: 2.855 > 0.409]: </pre>
3390it [00:04, 849.89it/s, bound: 7 | nc: 2 | ncall: 17200 | eff(%): 19.709 | loglstar: -inf < -9.665 < inf | logz: -18.779 +/- 0.143 | dlogz: 2.855 > 0.409]: end{sphinxVerbatim}

3561it [00:04, 1013.69it/s, bound: 7 | nc: 1 | ncall: 17459 | eff(%): 20.396 | loglstar: -inf < -8.855 < inf | logz: -18.064 +/- 0.143 | dlogz: 1.827 > 0.409]: </pre>
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3690it [00:04, 955.17it/s, bound: 7 | nc: 1 | ncall: 17717 | eff(%): 20.827 | loglstar: -inf < -8.455 < inf | logz: -17.685 +/- 0.143 | dlogz: 1.277 > 0.409]: </pre>
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3805it [00:05, 862.24it/s, bound: 8 | nc: 1 | ncall: 17913 | eff(%): 21.242 | loglstar: -inf < -8.248 < inf | logz: -17.436 +/- 0.143 | dlogz: 0.921 > 0.409]: </pre>
3805it [00:05, 862.24it/s, bound: 8 | nc: 1 | ncall: 17913 | eff(%): 21.242 | loglstar: -inf < -8.248 < inf | logz: -17.436 +/- 0.143 | dlogz: 0.921 > 0.409]: end{sphinxVerbatim}

3916it [00:05, 913.91it/s, bound: 8 | nc: 4 | ncall: 18104 | eff(%): 21.631 | loglstar: -inf < -8.091 < inf | logz: -17.261 +/- 0.143 | dlogz: 0.674 > 0.409]: </pre>
3916it [00:05, 913.91it/s, bound: 8 | nc: 4 | ncall: 18104 | eff(%): 21.631 | loglstar: -inf < -8.091 < inf | logz: -17.261 +/- 0.143 | dlogz: 0.674 > 0.409]: end{sphinxVerbatim}

4051it [00:05, 842.55it/s, bound: 9 | nc: 1 | ncall: 18402 | eff(%): 22.014 | loglstar: -inf < -7.931 < inf | logz: -17.105 +/- 0.143 | dlogz: 0.462 > 0.409]: </pre>
4051it [00:05, 842.55it/s, bound: 9 | nc: 1 | ncall: 18402 | eff(%): 22.014 | loglstar: -inf < -7.931 < inf | logz: -17.105 +/- 0.143 | dlogz: 0.462 > 0.409]: end{sphinxVerbatim}

4094it [00:05, 755.05it/s, +400 | bound: 9 | nc: 1 | ncall: 18849 | eff(%): 24.359 | loglstar: -inf < -7.527 < inf | logz: -16.711 +/- 0.143 | dlogz: 0.001 > 0.409]: </pre>
4094it [00:05, 755.05it/s, +400 | bound: 9 | nc: 1 | ncall: 18849 | eff(%): 24.359 | loglstar: -inf < -7.527 < inf | logz: -16.711 +/- 0.143 | dlogz: 0.001 > 0.409]: end{sphinxVerbatim}

18:25:53 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	1.015 -0.014 +0.015	1 / (cm2 keV s)
demo.spectrum.main.Sin.f	(9.96 +/- 0.05) x 10^-2	rad / keV

Values of -log(posterior) at the minimum:

	-log(posterior)
demo	-7.542081
total	-7.542081

Values of statistical measures:

	statistical measures
AIC	19.790044
BIC	21.075626
DIC	19.065969
PDIC	1.991506
log(Z)	-7.257289

[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()

18:25:54 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]

163it [00:00, 1628.98it/s, batch: 0 | bound: 0 | nc: 1 | ncall: 185 | eff(%): 23.796 | loglstar: -inf < -5523.364 < inf | logz: -5530.269 +/- 0.113 | dlogz: 5522.056 > 0.010]: </pre>
163it [00:00, 1628.98it/s, batch: 0 | bound: 0 | nc: 1 | ncall: 185 | eff(%): 23.796 | loglstar: -inf < -5523.364 < inf | logz: -5530.269 +/- 0.113 | dlogz: 5522.056 > 0.010]: end{sphinxVerbatim}

381it [00:00, 1950.82it/s, batch: 0 | bound: 0 | nc: 2 | ncall: 604 | eff(%): 34.511 | loglstar: -inf < -2419.411 < inf | logz: -2426.039 +/- 0.109 | dlogz: 2416.192 > 0.010]: </pre>
381it [00:00, 1950.82it/s, batch: 0 | bound: 0 | nc: 2 | ncall: 604 | eff(%): 34.511 | loglstar: -inf < -2419.411 < inf | logz: -2426.039 +/- 0.109 | dlogz: 2416.192 > 0.010]: end{sphinxVerbatim}

577it [00:00, 1671.30it/s, batch: 0 | bound: 0 | nc: 5 | ncall: 1175 | eff(%): 34.448 | loglstar: -inf < -2064.977 < inf | logz: -2072.757 +/- 0.121 | dlogz: 2063.852 > 0.010]: </pre>
577it [00:00, 1671.30it/s, batch: 0 | bound: 0 | nc: 5 | ncall: 1175 | eff(%): 34.448 | loglstar: -inf < -2064.977 < inf | logz: -2072.757 +/- 0.121 | dlogz: 2063.852 > 0.010]: end{sphinxVerbatim}

749it [00:00, 1544.90it/s, batch: 0 | bound: 0 | nc: 22 | ncall: 1960 | eff(%): 30.447 | loglstar: -inf < -1776.421 < inf | logz: -1784.640 +/- 0.125 | dlogz: 1777.512 > 0.010]: </pre>
749it [00:00, 1544.90it/s, batch: 0 | bound: 0 | nc: 22 | ncall: 1960 | eff(%): 30.447 | loglstar: -inf < -1776.421 < inf | logz: -1784.640 +/- 0.125 | dlogz: 1777.512 > 0.010]: end{sphinxVerbatim}

907it [00:00, 1246.94it/s, batch: 0 | bound: 0 | nc: 5 | ncall: 3006 | eff(%): 25.870 | loglstar: -inf < -1577.259 < inf | logz: -1584.729 +/- 0.118 | dlogz: 1575.993 > 0.010]: </pre>
907it [00:00, 1246.94it/s, batch: 0 | bound: 0 | nc: 5 | ncall: 3006 | eff(%): 25.870 | loglstar: -inf < -1577.259 < inf | logz: -1584.729 +/- 0.118 | dlogz: 1575.993 > 0.010]: end{sphinxVerbatim}

1040it [00:00, 1044.92it/s, batch: 0 | bound: 0 | nc: 68 | ncall: 4226 | eff(%): 22.006 | loglstar: -inf < -1137.603 < inf | logz: -1146.573 +/- 0.133 | dlogz: 1141.617 > 0.010]: </pre>
1040it [00:00, 1044.92it/s, batch: 0 | bound: 0 | nc: 68 | ncall: 4226 | eff(%): 22.006 | loglstar: -inf < -1137.603 < inf | logz: -1146.573 +/- 0.133 | dlogz: 1141.617 > 0.010]: end{sphinxVerbatim}

1153it [00:00, 930.81it/s, batch: 0 | bound: 0 | nc: 11 | ncall: 5526 | eff(%): 19.134 | loglstar: -inf < -825.714 < inf | logz: -834.531 +/- 0.129 | dlogz: 826.328 > 0.010]: </pre>
1153it [00:00, 930.81it/s, batch: 0 | bound: 0 | nc: 11 | ncall: 5526 | eff(%): 19.134 | loglstar: -inf < -825.714 < inf | logz: -834.531 +/- 0.129 | dlogz: 826.328 > 0.010]: end{sphinxVerbatim}

1252it [00:01, 784.63it/s, batch: 0 | bound: 0 | nc: 6 | ncall: 6838 | eff(%): 17.062 | loglstar: -inf < -653.115 < inf | logz: -661.976 +/- 0.127 | dlogz: 653.050 > 0.010]: </pre>
1252it [00:01, 784.63it/s, batch: 0 | bound: 0 | nc: 6 | ncall: 6838 | eff(%): 17.062 | loglstar: -inf < -653.115 < inf | logz: -661.976 +/- 0.127 | dlogz: 653.050 > 0.010]: end{sphinxVerbatim}

1337it [00:01, 652.54it/s, batch: 0 | bound: 0 | nc: 57 | ncall: 8362 | eff(%): 15.087 | loglstar: -inf < -566.862 < inf | logz: -575.809 +/- 0.127 | dlogz: 566.597 > 0.010]: </pre>
1337it [00:01, 652.54it/s, batch: 0 | bound: 0 | nc: 57 | ncall: 8362 | eff(%): 15.087 | loglstar: -inf < -566.862 < inf | logz: -575.809 +/- 0.127 | dlogz: 566.597 > 0.010]: end{sphinxVerbatim}

1408it [00:01, 537.04it/s, batch: 0 | bound: 0 | nc: 125 | ncall: 9967 | eff(%): 13.452 | loglstar: -inf < -494.244 < inf | logz: -503.139 +/- 0.128 | dlogz: 493.475 > 0.010]: </pre>
1408it [00:01, 537.04it/s, batch: 0 | bound: 0 | nc: 125 | ncall: 9967 | eff(%): 13.452 | loglstar: -inf < -494.244 < inf | logz: -503.139 +/- 0.128 | dlogz: 493.475 > 0.010]: end{sphinxVerbatim}

1468it [00:01, 490.86it/s, batch: 0 | bound: 0 | nc: 24 | ncall: 11078 | eff(%): 12.679 | loglstar: -inf < -439.077 < inf | logz: -448.038 +/- 0.129 | dlogz: 438.472 > 0.010]: </pre>
1468it [00:01, 490.86it/s, batch: 0 | bound: 0 | nc: 24 | ncall: 11078 | eff(%): 12.679 | loglstar: -inf < -439.077 < inf | logz: -448.038 +/- 0.129 | dlogz: 438.472 > 0.010]: end{sphinxVerbatim}

1521it [00:01, 429.16it/s, batch: 0 | bound: 0 | nc: 1 | ncall: 12390 | eff(%): 11.800 | loglstar: -inf < -399.747 < inf | logz: -408.363 +/- 0.123 | dlogz: 398.120 > 0.010]: </pre>
1521it [00:01, 429.16it/s, batch: 0 | bound: 0 | nc: 1 | ncall: 12390 | eff(%): 11.800 | loglstar: -inf < -399.747 < inf | logz: -408.363 +/- 0.123 | dlogz: 398.120 > 0.010]: end{sphinxVerbatim}

1567it [00:02, 387.63it/s, batch: 0 | bound: 0 | nc: 5 | ncall: 13600 | eff(%): 11.113 | loglstar: -inf < -368.514 < inf | logz: -377.004 +/- 0.124 | dlogz: 366.632 > 0.010]: </pre>
1567it [00:02, 387.63it/s, batch: 0 | bound: 0 | nc: 5 | ncall: 13600 | eff(%): 11.113 | loglstar: -inf < -368.514 < inf | logz: -377.004 +/- 0.124 | dlogz: 366.632 > 0.010]: end{sphinxVerbatim}

1607it [00:02, 354.38it/s, batch: 0 | bound: 0 | nc: 80 | ncall: 14926 | eff(%): 10.417 | loglstar: -inf < -350.825 < inf | logz: -359.269 +/- 0.124 | dlogz: 348.760 > 0.010]: </pre>
1607it [00:02, 354.38it/s, batch: 0 | bound: 0 | nc: 80 | ncall: 14926 | eff(%): 10.417 | loglstar: -inf < -350.825 < inf | logz: -359.269 +/- 0.124 | dlogz: 348.760 > 0.010]: end{sphinxVerbatim}

1643it [00:02, 352.18it/s, batch: 0 | bound: 0 | nc: 37 | ncall: 15687 | eff(%): 10.150 | loglstar: -inf < -323.381 < inf | logz: -332.079 +/- 0.129 | dlogz: 321.667 > 0.010]: </pre>
1643it [00:02, 352.18it/s, batch: 0 | bound: 0 | nc: 37 | ncall: 15687 | eff(%): 10.150 | loglstar: -inf < -323.381 < inf | logz: -332.079 +/- 0.129 | dlogz: 321.667 > 0.010]: end{sphinxVerbatim}

1679it [00:02, 297.72it/s, batch: 0 | bound: 1 | nc: 1 | ncall: 16123 | eff(%): 10.100 | loglstar: -inf < -300.458 < inf | logz: -309.258 +/- 0.124 | dlogz: 298.666 > 0.010]: </pre>
1679it [00:02, 297.72it/s, batch: 0 | bound: 1 | nc: 1 | ncall: 16123 | eff(%): 10.100 | loglstar: -inf < -300.458 < inf | logz: -309.258 +/- 0.124 | dlogz: 298.666 > 0.010]: end{sphinxVerbatim}

1884it [00:02, 668.46it/s, batch: 0 | bound: 1 | nc: 2 | ncall: 16442 | eff(%): 11.120 | loglstar: -inf < -208.766 < inf | logz: -217.768 +/- 0.129 | dlogz: 206.791 > 0.010]: </pre>
1884it [00:02, 668.46it/s, batch: 0 | bound: 1 | nc: 2 | ncall: 16442 | eff(%): 11.120 | loglstar: -inf < -208.766 < inf | logz: -217.768 +/- 0.129 | dlogz: 206.791 > 0.010]: end{sphinxVerbatim}

2037it [00:02, 867.80it/s, batch: 0 | bound: 1 | nc: 1 | ncall: 16824 | eff(%): 11.758 | loglstar: -inf < -158.329 < inf | logz: -167.027 +/- 0.125 | dlogz: 155.503 > 0.010]: </pre>
2037it [00:02, 867.80it/s, batch: 0 | bound: 1 | nc: 1 | ncall: 16824 | eff(%): 11.758 | loglstar: -inf < -158.329 < inf | logz: -167.027 +/- 0.125 | dlogz: 155.503 > 0.010]: end{sphinxVerbatim}

2141it [00:02, 765.62it/s, batch: 0 | bound: 2 | nc: 1 | ncall: 16979 | eff(%): 12.249 | loglstar: -inf < -130.868 < inf | logz: -140.199 +/- 0.128 | dlogz: 128.544 > 0.010]: </pre>
2141it [00:02, 765.62it/s, batch: 0 | bound: 2 | nc: 1 | ncall: 16979 | eff(%): 12.249 | loglstar: -inf < -130.868 < inf | logz: -140.199 +/- 0.128 | dlogz: 128.544 > 0.010]: end{sphinxVerbatim}

2360it [00:03, 1092.51it/s, batch: 0 | bound: 2 | nc: 3 | ncall: 17393 | eff(%): 13.190 | loglstar: -inf < -85.750 < inf | logz: -94.326 +/- 0.125 | dlogz: 82.064 > 0.010]: </pre>
2360it [00:03, 1092.51it/s, batch: 0 | bound: 2 | nc: 3 | ncall: 17393 | eff(%): 13.190 | loglstar: -inf < -85.750 < inf | logz: -94.326 +/- 0.125 | dlogz: 82.064 > 0.010]: end{sphinxVerbatim}

2489it [00:03, 919.47it/s, batch: 0 | bound: 3 | nc: 1 | ncall: 17649 | eff(%): 13.714 | loglstar: -inf < -68.758 < inf | logz: -77.731 +/- 0.126 | dlogz: 65.220 > 0.010]: </pre>
2489it [00:03, 919.47it/s, batch: 0 | bound: 3 | nc: 1 | ncall: 17649 | eff(%): 13.714 | loglstar: -inf < -68.758 < inf | logz: -77.731 +/- 0.126 | dlogz: 65.220 > 0.010]: end{sphinxVerbatim}

2680it [00:03, 1138.32it/s, batch: 0 | bound: 3 | nc: 1 | ncall: 17929 | eff(%): 14.542 | loglstar: -inf < -50.059 < inf | logz: -58.941 +/- 0.127 | dlogz: 46.009 > 0.010]: </pre>
2680it [00:03, 1138.32it/s, batch: 0 | bound: 3 | nc: 1 | ncall: 17929 | eff(%): 14.542 | loglstar: -inf < -50.059 < inf | logz: -58.941 +/- 0.127 | dlogz: 46.009 > 0.010]: end{sphinxVerbatim}

2835it [00:03, 1234.55it/s, batch: 0 | bound: 3 | nc: 6 | ncall: 18279 | eff(%): 15.097 | loglstar: -inf < -39.267 < inf | logz: -48.430 +/- 0.128 | dlogz: 35.187 > 0.010]: </pre>
2835it [00:03, 1234.55it/s, batch: 0 | bound: 3 | nc: 6 | ncall: 18279 | eff(%): 15.097 | loglstar: -inf < -39.267 < inf | logz: -48.430 +/- 0.128 | dlogz: 35.187 > 0.010]: end{sphinxVerbatim}

2975it [00:03, 1029.81it/s, batch: 0 | bound: 4 | nc: 1 | ncall: 18488 | eff(%): 15.668 | loglstar: -inf < -31.465 < inf | logz: -40.553 +/- 0.127 | dlogz: 27.011 > 0.010]: </pre>
2975it [00:03, 1029.81it/s, batch: 0 | bound: 4 | nc: 1 | ncall: 18488 | eff(%): 15.668 | loglstar: -inf < -31.465 < inf | logz: -40.553 +/- 0.127 | dlogz: 27.011 > 0.010]: end{sphinxVerbatim}

3177it [00:03, 1254.69it/s, batch: 0 | bound: 4 | nc: 1 | ncall: 18812 | eff(%): 16.451 | loglstar: -inf < -24.282 < inf | logz: -33.496 +/- 0.127 | dlogz: 19.659 > 0.010]: </pre>
3177it [00:03, 1254.69it/s, batch: 0 | bound: 4 | nc: 1 | ncall: 18812 | eff(%): 16.451 | loglstar: -inf < -24.282 < inf | logz: -33.496 +/- 0.127 | dlogz: 19.659 > 0.010]: end{sphinxVerbatim}

3322it [00:03, 1012.42it/s, batch: 0 | bound: 5 | nc: 1 | ncall: 19137 | eff(%): 16.917 | loglstar: -inf < -19.884 < inf | logz: -29.007 +/- 0.128 | dlogz: 14.869 > 0.010]: </pre>
3322it [00:03, 1012.42it/s, batch: 0 | bound: 5 | nc: 1 | ncall: 19137 | eff(%): 16.917 | loglstar: -inf < -19.884 < inf | logz: -29.007 +/- 0.128 | dlogz: 14.869 > 0.010]: end{sphinxVerbatim}

3471it [00:04, 1114.01it/s, batch: 0 | bound: 5 | nc: 1 | ncall: 19331 | eff(%): 17.503 | loglstar: -inf < -16.526 < inf | logz: -25.668 +/- 0.128 | dlogz: 11.226 > 0.010]: </pre>
3471it [00:04, 1114.01it/s, batch: 0 | bound: 5 | nc: 1 | ncall: 19331 | eff(%): 17.503 | loglstar: -inf < -16.526 < inf | logz: -25.668 +/- 0.128 | dlogz: 11.226 > 0.010]: end{sphinxVerbatim}

3646it [00:04, 1262.05it/s, batch: 0 | bound: 5 | nc: 4 | ncall: 19677 | eff(%): 18.070 | loglstar: -inf < -14.094 < inf | logz: -23.105 +/- 0.127 | dlogz: 8.307 > 0.010]: </pre>
3646it [00:04, 1262.05it/s, batch: 0 | bound: 5 | nc: 4 | ncall: 19677 | eff(%): 18.070 | loglstar: -inf < -14.094 < inf | logz: -23.105 +/- 0.127 | dlogz: 8.307 > 0.010]: end{sphinxVerbatim}

3789it [00:04, 1011.01it/s, batch: 0 | bound: 6 | nc: 2 | ncall: 19916 | eff(%): 18.559 | loglstar: -inf < -12.712 < inf | logz: -21.697 +/- 0.127 | dlogz: 6.612 > 0.010]: </pre>
3789it [00:04, 1011.01it/s, batch: 0 | bound: 6 | nc: 2 | ncall: 19916 | eff(%): 18.559 | loglstar: -inf < -12.712 < inf | logz: -21.697 +/- 0.127 | dlogz: 6.612 > 0.010]: end{sphinxVerbatim}

4040it [00:04, 1335.90it/s, batch: 0 | bound: 6 | nc: 1 | ncall: 20269 | eff(%): 19.452 | loglstar: -inf < -10.629 < inf | logz: -19.910 +/- 0.127 | dlogz: 4.334 > 0.010]: </pre>
4040it [00:04, 1335.90it/s, batch: 0 | bound: 6 | nc: 1 | ncall: 20269 | eff(%): 19.452 | loglstar: -inf < -10.629 < inf | logz: -19.910 +/- 0.127 | dlogz: 4.334 > 0.010]: end{sphinxVerbatim}

4200it [00:04, 1063.69it/s, batch: 0 | bound: 7 | nc: 1 | ncall: 20646 | eff(%): 19.862 | loglstar: -inf < -9.843 < inf | logz: -19.025 +/- 0.128 | dlogz: 3.157 > 0.010]: </pre>
4200it [00:04, 1063.69it/s, batch: 0 | bound: 7 | nc: 1 | ncall: 20646 | eff(%): 19.862 | loglstar: -inf < -9.843 < inf | logz: -19.025 +/- 0.128 | dlogz: 3.157 > 0.010]: end{sphinxVerbatim}

4409it [00:04, 1273.55it/s, batch: 0 | bound: 7 | nc: 3 | ncall: 20951 | eff(%): 20.554 | loglstar: -inf < -9.069 < inf | logz: -18.281 +/- 0.128 | dlogz: 2.083 > 0.010]: </pre>
4409it [00:04, 1273.55it/s, batch: 0 | bound: 7 | nc: 3 | ncall: 20951 | eff(%): 20.554 | loglstar: -inf < -9.069 < inf | logz: -18.281 +/- 0.128 | dlogz: 2.083 > 0.010]: end{sphinxVerbatim}

4594it [00:05, 1103.49it/s, batch: 0 | bound: 8 | nc: 1 | ncall: 21366 | eff(%): 21.010 | loglstar: -inf < -8.554 < inf | logz: -17.812 +/- 0.128 | dlogz: 1.396 > 0.010]: </pre>
4594it [00:05, 1103.49it/s, batch: 0 | bound: 8 | nc: 1 | ncall: 21366 | eff(%): 21.010 | loglstar: -inf < -8.554 < inf | logz: -17.812 +/- 0.128 | dlogz: 1.396 > 0.010]: end{sphinxVerbatim}

4793it [00:05, 1282.08it/s, batch: 0 | bound: 8 | nc: 1 | ncall: 21667 | eff(%): 21.622 | loglstar: -inf < -8.204 < inf | logz: -17.456 +/- 0.128 | dlogz: 0.888 > 0.010]: </pre>
4793it [00:05, 1282.08it/s, batch: 0 | bound: 8 | nc: 1 | ncall: 21667 | eff(%): 21.622 | loglstar: -inf < -8.204 < inf | logz: -17.456 +/- 0.128 | dlogz: 0.888 > 0.010]: end{sphinxVerbatim}

4984it [00:05, 1421.37it/s, batch: 0 | bound: 8 | nc: 3 | ncall: 22035 | eff(%): 22.117 | loglstar: -inf < -7.968 < inf | logz: -17.224 +/- 0.128 | dlogz: 0.573 > 0.010]: </pre>
4984it [00:05, 1421.37it/s, batch: 0 | bound: 8 | nc: 3 | ncall: 22035 | eff(%): 22.117 | loglstar: -inf < -7.968 < inf | logz: -17.224 +/- 0.128 | dlogz: 0.573 > 0.010]: end{sphinxVerbatim}

5149it [00:05, 1146.83it/s, batch: 0 | bound: 9 | nc: 1 | ncall: 22272 | eff(%): 22.611 | loglstar: -inf < -7.829 < inf | logz: -17.085 +/- 0.128 | dlogz: 0.395 > 0.010]: </pre>
5149it [00:05, 1146.83it/s, batch: 0 | bound: 9 | nc: 1 | ncall: 22272 | eff(%): 22.611 | loglstar: -inf < -7.829 < inf | logz: -17.085 +/- 0.128 | dlogz: 0.395 > 0.010]: end{sphinxVerbatim}

5323it [00:05, 1272.17it/s, batch: 0 | bound: 9 | nc: 1 | ncall: 22556 | eff(%): 23.087 | loglstar: -inf < -7.739 < inf | logz: -16.981 +/- 0.128 | dlogz: 0.269 > 0.010]: </pre>
5323it [00:05, 1272.17it/s, batch: 0 | bound: 9 | nc: 1 | ncall: 22556 | eff(%): 23.087 | loglstar: -inf < -7.739 < inf | logz: -16.981 +/- 0.128 | dlogz: 0.269 > 0.010]: end{sphinxVerbatim}

5472it [00:05, 1051.47it/s, batch: 0 | bound: 10 | nc: 1 | ncall: 22871 | eff(%): 23.414 | loglstar: -inf < -7.691 < inf | logz: -16.918 +/- 0.128 | dlogz: 0.195 > 0.010]: </pre>
5472it [00:05, 1051.47it/s, batch: 0 | bound: 10 | nc: 1 | ncall: 22871 | eff(%): 23.414 | loglstar: -inf < -7.691 < inf | logz: -16.918 +/- 0.128 | dlogz: 0.195 > 0.010]: end{sphinxVerbatim}

5675it [00:05, 1255.61it/s, batch: 0 | bound: 10 | nc: 1 | ncall: 23136 | eff(%): 24.010 | loglstar: -inf < -7.632 < inf | logz: -16.857 +/- 0.128 | dlogz: 0.126 > 0.010]: </pre>
5675it [00:05, 1255.61it/s, batch: 0 | bound: 10 | nc: 1 | ncall: 23136 | eff(%): 24.010 | loglstar: -inf < -7.632 < inf | logz: -16.857 +/- 0.128 | dlogz: 0.126 > 0.010]: end{sphinxVerbatim}

5876it [00:05, 1426.74it/s, batch: 0 | bound: 10 | nc: 8 | ncall: 23516 | eff(%): 24.467 | loglstar: -inf < -7.600 < inf | logz: -16.817 +/- 0.128 | dlogz: 0.083 > 0.010]: </pre>
5876it [00:05, 1426.74it/s, batch: 0 | bound: 10 | nc: 8 | ncall: 23516 | eff(%): 24.467 | loglstar: -inf < -7.600 < inf | logz: -16.817 +/- 0.128 | dlogz: 0.083 > 0.010]: end{sphinxVerbatim}

6040it [00:06, 1201.48it/s, batch: 0 | bound: 11 | nc: 1 | ncall: 23759 | eff(%): 24.898 | loglstar: -inf < -7.582 < inf | logz: -16.795 +/- 0.128 | dlogz: 0.059 > 0.010]: </pre>
6040it [00:06, 1201.48it/s, batch: 0 | bound: 11 | nc: 1 | ncall: 23759 | eff(%): 24.898 | loglstar: -inf < -7.582 < inf | logz: -16.795 +/- 0.128 | dlogz: 0.059 > 0.010]: end{sphinxVerbatim}

6231it [00:06, 1358.03it/s, batch: 0 | bound: 11 | nc: 1 | ncall: 24040 | eff(%): 25.391 | loglstar: -inf < -7.565 < inf | logz: -16.777 +/- 0.128 | dlogz: 0.040 > 0.010]: </pre>
6231it [00:06, 1358.03it/s, batch: 0 | bound: 11 | nc: 1 | ncall: 24040 | eff(%): 25.391 | loglstar: -inf < -7.565 < inf | logz: -16.777 +/- 0.128 | dlogz: 0.040 > 0.010]: end{sphinxVerbatim}

6394it [00:06, 847.26it/s, batch: 0 | bound: 12 | nc: 1 | ncall: 24376 | eff(%): 25.703 | loglstar: -inf < -7.554 < inf | logz: -16.766 +/- 0.128 | dlogz: 0.029 > 0.010]: </pre>
6394it [00:06, 847.26it/s, batch: 0 | bound: 12 | nc: 1 | ncall: 24376 | eff(%): 25.703 | loglstar: -inf < -7.554 < inf | logz: -16.766 +/- 0.128 | dlogz: 0.029 > 0.010]: end{sphinxVerbatim}

6525it [00:06, 925.67it/s, batch: 0 | bound: 12 | nc: 3 | ncall: 24532 | eff(%): 26.067 | loglstar: -inf < -7.547 < inf | logz: -16.759 +/- 0.128 | dlogz: 0.022 > 0.010]: </pre>
6525it [00:06, 925.67it/s, batch: 0 | bound: 12 | nc: 3 | ncall: 24532 | eff(%): 26.067 | loglstar: -inf < -7.547 < inf | logz: -16.759 +/- 0.128 | dlogz: 0.022 > 0.010]: end{sphinxVerbatim}

6678it [00:06, 1043.23it/s, batch: 0 | bound: 12 | nc: 1 | ncall: 24794 | eff(%): 26.402 | loglstar: -inf < -7.542 < inf | logz: -16.753 +/- 0.128 | dlogz: 0.016 > 0.010]: </pre>
6678it [00:06, 1043.23it/s, batch: 0 | bound: 12 | nc: 1 | ncall: 24794 | eff(%): 26.402 | loglstar: -inf < -7.542 < inf | logz: -16.753 +/- 0.128 | dlogz: 0.016 > 0.010]: end{sphinxVerbatim}

6814it [00:06, 1071.05it/s, batch: 0 | bound: 12 | nc: 10 | ncall: 25102 | eff(%): 26.615 | loglstar: -inf < -7.538 < inf | logz: -16.750 +/- 0.128 | dlogz: 0.012 > 0.010]: </pre>
6814it [00:06, 1071.05it/s, batch: 0 | bound: 12 | nc: 10 | ncall: 25102 | eff(%): 26.615 | loglstar: -inf < -7.538 < inf | logz: -16.750 +/- 0.128 | dlogz: 0.012 > 0.010]: end{sphinxVerbatim}

6942it [00:07, 860.93it/s, batch: 0 | bound: 13 | nc: 1 | ncall: 25264 | eff(%): 26.969 | loglstar: -inf < -7.536 < inf | logz: -16.747 +/- 0.128 | dlogz: 0.010 > 0.010]: </pre>
6942it [00:07, 860.93it/s, batch: 0 | bound: 13 | nc: 1 | ncall: 25264 | eff(%): 26.969 | loglstar: -inf < -7.536 < inf | logz: -16.747 +/- 0.128 | dlogz: 0.010 > 0.010]: end{sphinxVerbatim}


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

7419it [00:08, 489.65it/s, batch: 1 | bound: 0 | nc: 1 | ncall: 25741 | eff(%): 28.822 | loglstar: -9.224 < -7.706 < -7.971 | logz: -16.737 +/- 0.132 | stop: 1.529]: </pre>
7419it [00:08, 489.65it/s, batch: 1 | bound: 0 | nc: 1 | ncall: 25741 | eff(%): 28.822 | loglstar: -9.224 < -7.706 < -7.971 | logz: -16.737 +/- 0.132 | stop: 1.529]: end{sphinxVerbatim}

7515it [00:08, 525.54it/s, batch: 1 | bound: 2 | nc: 1 | ncall: 25853 | eff(%): 28.497 | loglstar: -9.224 < -8.947 < -7.971 | logz: -16.737 +/- 0.132 | stop: 1.529]: </pre>
7515it [00:08, 525.54it/s, batch: 1 | bound: 2 | nc: 1 | ncall: 25853 | eff(%): 28.497 | loglstar: -9.224 < -8.947 < -7.971 | logz: -16.737 +/- 0.132 | stop: 1.529]: end{sphinxVerbatim}

7603it [00:08, 540.39it/s, batch: 1 | bound: 2 | nc: 1 | ncall: 25975 | eff(%): 28.698 | loglstar: -9.224 < -8.679 < -7.971 | logz: -16.737 +/- 0.132 | stop: 1.529]: </pre>
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18:26:06 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	1.016 +/- 0.014	1 / (cm2 keV s)
demo.spectrum.main.Sin.f	(9.96 -0.05 +0.06) x 10^-2	rad / keV

Values of -log(posterior) at the minimum:

	-log(posterior)
demo	-7.540926
total	-7.540926

Values of statistical measures:

	statistical measures
AIC	19.787735
BIC	21.073317
DIC	19.046044
PDIC	1.981413
log(Z)	-7.271178

[8]:

../_images/notebooks_sampler_docs_12_72.png

../_images/notebooks_sampler_docs_12_73.png

../_images/notebooks_sampler_docs_12_74.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()

18:26:07 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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18:26:22 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: 27

Scale Factor: 1.090164

Mean Integrated Autocorrelation Time: 3.21

Effective Sample Size: 3896.6

Number of Log Probability Evaluations: 65363

Effective Samples per Log Probability Evaluation: 0.059615

None

Maximum a posteriori probability (MAP) point:

	result	unit
parameter
demo.spectrum.main.Sin.K	1.016 +/- 0.014	1 / (cm2 keV s)
demo.spectrum.main.Sin.f	(9.96 -0.05 +0.06) x 10^-2	rad / keV

Values of -log(posterior) at the minimum:

	-log(posterior)
demo	-7.541031
total	-7.541031

Values of statistical measures:

	statistical measures
AIC	19.787944
BIC	21.073526
DIC	19.121326
PDIC	2.017930

[9]:

../_images/notebooks_sampler_docs_14_136.png

../_images/notebooks_sampler_docs_14_137.png

../_images/notebooks_sampler_docs_14_138.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()

18:26:24 INFO      sampler set to ultranest                                                bayesian_analysis.py:202

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

Z=-inf(0.00%) | Like=-16809.60..-35.09 [-16809.5981..-2710.9353] | it/evals=0/401 eff=0.0000% N=400

Z=-9993.3(0.00%) | Like=-9824.66..-35.09 [-16809.5981..-2710.9353] | it/evals=40/443 eff=93.0233% N=400

Z=-7492.9(0.00%) | Like=-7329.63..-35.09 [-16809.5981..-2710.9353] | it/evals=80/487 eff=91.9540% N=400

Z=-7000.6(0.00%) | Like=-6900.23..-35.09 [-16809.5981..-2710.9353] | it/evals=90/498 eff=91.8367% N=400

Z=-6207.0(0.00%) | Like=-6175.31..-35.09 [-16809.5981..-2710.9353] | it/evals=120/536 eff=88.2353% N=400

Z=-5065.9(0.00%) | Like=-5033.86..-35.09 [-16809.5981..-2710.9353] | it/evals=160/592 eff=83.3333% N=400

Z=-4505.0(0.00%) | Like=-4472.14..-35.09 [-16809.5981..-2710.9353] | it/evals=180/622 eff=81.0811% N=400

Z=-4087.0(0.00%) | Like=-4045.43..-35.09 [-16809.5981..-2710.9353] | it/evals=200/644 eff=81.9672% N=400

Z=-3227.7(0.00%) | Like=-3202.41..-35.09 [-16809.5981..-2710.9353] | it/evals=240/698 eff=80.5369% N=400

Z=-2839.4(0.00%) | Like=-2811.00..-35.09 [-16809.5981..-2710.9353] | it/evals=265/731 eff=80.0604% N=400

Z=-2790.3(0.00%) | Like=-2777.97..-35.09 [-16809.5981..-2710.9353] | it/evals=270/736 eff=80.3571% N=400

Z=-2725.3(0.00%) | Like=-2703.25..-35.09 [-2703.2490..-1988.2735] | it/evals=280/748 eff=80.4598% N=400

Z=-2533.3(0.00%) | Like=-2510.61..-35.09 [-2703.2490..-1988.2735] | it/evals=320/798 eff=80.4020% N=400

Z=-2451.3(0.00%) | Like=-2440.77..-35.09 [-2703.2490..-1988.2735] | it/evals=344/838 eff=78.5388% N=400

Z=-2427.9(0.00%) | Like=-2420.24..-35.09 [-2703.2490..-1988.2735] | it/evals=356/859 eff=77.5599% N=400

Z=-2421.1(0.00%) | Like=-2413.08..-35.09 [-2703.2490..-1988.2735] | it/evals=360/864 eff=77.5862% N=400

Z=-2282.7(0.00%) | Like=-2274.90..-35.09 [-2703.2490..-1988.2735] | it/evals=400/931 eff=75.3296% N=400

Z=-2212.0(0.00%) | Like=-2204.79..-35.09 [-2703.2490..-1988.2735] | it/evals=440/1012 eff=71.8954% N=400

Z=-2154.8(0.00%) | Like=-2146.35..-35.09 [-2703.2490..-1988.2735] | it/evals=480/1098 eff=68.7679% N=400

Z=-2081.7(0.00%) | Like=-2073.91..-35.09 [-2703.2490..-1988.2735] | it/evals=520/1184 eff=66.3265% N=400

Z=-2053.1(0.00%) | Like=-2046.04..-35.09 [-2703.2490..-1988.2735] | it/evals=540/1234 eff=64.7482% N=400

Z=-2021.2(0.00%) | Like=-2011.69..-35.09 [-2703.2490..-1988.2735] | it/evals=560/1296 eff=62.5000% N=400

Z=-1996.0(0.00%) | Like=-1988.33..-35.09 [-2703.2490..-1988.2735] | it/evals=575/1357 eff=60.0836% N=400

Z=-1986.3(0.00%) | Like=-1977.52..-35.09 [-1988.2123..-1563.1980] | it/evals=582/1386 eff=59.0264% N=400

Z=-1965.2(0.00%) | Like=-1957.19..-8.26 [-1988.2123..-1563.1980] | it/evals=600/1440 eff=57.6923% N=400

Z=-1911.9(0.00%) | Like=-1903.31..-8.26 [-1988.2123..-1563.1980] | it/evals=630/1539 eff=55.3117% N=400

Z=-1901.1(0.00%) | Like=-1892.05..-8.26 [-1988.2123..-1563.1980] | it/evals=640/1573 eff=54.5610% N=400

Z=-1813.0(0.00%) | Like=-1797.72..-8.26 [-1988.2123..-1563.1980] | it/evals=680/1724 eff=51.3595% N=400

Z=-1794.6(0.00%) | Like=-1786.55..-8.26 [-1988.2123..-1563.1980] | it/evals=687/1752 eff=50.8136% N=400

Z=-1756.2(0.00%) | Like=-1747.67..-8.26 [-1988.2123..-1563.1980] | it/evals=703/1822 eff=49.4374% N=400

Z=-1725.9(0.00%) | Like=-1718.20..-8.26 [-1988.2123..-1563.1980] | it/evals=720/1866 eff=49.1132% N=400

Z=-1660.3(0.00%) | Like=-1652.29..-8.26 [-1988.2123..-1563.1980] | it/evals=760/1928 eff=49.7382% N=400

Z=-1610.3(0.00%) | Like=-1600.94..-8.26 [-1988.2123..-1563.1980] | it/evals=800/2035 eff=48.9297% N=400

Z=-1591.1(0.00%) | Like=-1583.35..-8.26 [-1988.2123..-1563.1980] | it/evals=818/2094 eff=48.2881% N=400

Z=-1583.4(0.00%) | Like=-1571.80..-8.26 [-1988.2123..-1563.1980] | it/evals=829/2123 eff=48.1138% N=400

Z=-1573.7(0.00%) | Like=-1565.42..-8.26 [-1988.2123..-1563.1980] | it/evals=840/2156 eff=47.8360% N=400

Z=-1439.7(0.00%) | Like=-1429.23..-8.26 [-1561.4903..-679.6380] | it/evals=880/2275 eff=46.9333% N=400

Z=-1367.2(0.00%) | Like=-1357.28..-8.26 [-1561.4903..-679.6380] | it/evals=900/2342 eff=46.3440% N=400

Z=-1291.6(0.00%) | Like=-1277.46..-8.26 [-1561.4903..-679.6380] | it/evals=920/2368 eff=46.7480% N=400

Z=-1174.2(0.00%) | Like=-1164.68..-8.26 [-1561.4903..-679.6380] | it/evals=960/2426 eff=47.3840% N=400

Z=-1052.3(0.00%) | Like=-1042.18..-8.26 [-1561.4903..-679.6380] | it/evals=990/2469 eff=47.8492% N=400

Z=-1011.2(0.00%) | Like=-996.48..-8.26 [-1561.4903..-679.6380] | it/evals=1000/2481 eff=48.0538% N=400

Z=-859.7(0.00%) | Like=-848.20..-8.26 [-1561.4903..-679.6380] | it/evals=1040/2530 eff=48.8263% N=400

Z=-778.6(0.00%) | Like=-767.67..-8.26 [-1561.4903..-679.6380] | it/evals=1080/2588 eff=49.3601% N=400

Z=-691.7(0.00%) | Like=-681.33..-8.26 [-1561.4903..-679.6380] | it/evals=1120/2636 eff=50.0894% N=400

Z=-635.8(0.00%) | Like=-627.62..-8.26 [-679.5805..-373.4322] | it/evals=1160/2690 eff=50.6550% N=400

Z=-619.8(0.00%) | Like=-610.15..-8.26 [-679.5805..-373.4322] | it/evals=1170/2703 eff=50.8033% N=400

Z=-580.8(0.00%) | Like=-571.34..-8.26 [-679.5805..-373.4322] | it/evals=1200/2745 eff=51.1727% N=400

Z=-524.3(0.00%) | Like=-513.74..-8.26 [-679.5805..-373.4322] | it/evals=1240/2802 eff=51.6236% N=400

Z=-501.9(0.00%) | Like=-491.59..-8.26 [-679.5805..-373.4322] | it/evals=1260/2824 eff=51.9802% N=400

Z=-484.0(0.00%) | Like=-475.21..-8.26 [-679.5805..-373.4322] | it/evals=1280/2848 eff=52.2876% N=400

Z=-444.3(0.00%) | Like=-435.41..-8.26 [-679.5805..-373.4322] | it/evals=1320/2907 eff=52.6526% N=400

Z=-421.7(0.00%) | Like=-412.65..-8.26 [-679.5805..-373.4322] | it/evals=1350/2956 eff=52.8169% N=400

Z=-411.4(0.00%) | Like=-402.14..-8.26 [-679.5805..-373.4322] | it/evals=1360/2970 eff=52.9183% N=400

Z=-371.6(0.00%) | Like=-362.54..-8.26 [-373.0308..-201.1066] | it/evals=1400/3029 eff=53.2522% N=400

Z=-342.5(0.00%) | Like=-333.69..-8.26 [-373.0308..-201.1066] | it/evals=1440/3090 eff=53.5316% N=400

Z=-307.7(0.00%) | Like=-297.88..-8.26 [-373.0308..-201.1066] | it/evals=1480/3150 eff=53.8182% N=400

Z=-281.9(0.00%) | Like=-272.61..-8.26 [-373.0308..-201.1066] | it/evals=1520/3230 eff=53.7102% N=400

Z=-276.8(0.00%) | Like=-267.53..-8.26 [-373.0308..-201.1066] | it/evals=1530/3246 eff=53.7597% N=400

Z=-257.7(0.00%) | Like=-248.19..-8.26 [-373.0308..-201.1066] | it/evals=1560/3292 eff=53.9419% N=400

Z=-237.9(0.00%) | Like=-228.11..-8.26 [-373.0308..-201.1066] | it/evals=1600/3354 eff=54.1638% N=400

Z=-227.5(0.00%) | Like=-217.76..-8.26 [-373.0308..-201.1066] | it/evals=1620/3385 eff=54.2714% N=400

Z=-214.9(0.00%) | Like=-205.70..-8.26 [-373.0308..-201.1066] | it/evals=1640/3413 eff=54.4308% N=400

Z=-198.9(0.00%) | Like=-189.32..-8.01 [-200.9572..-109.8084] | it/evals=1680/3466 eff=54.7945% N=400

Z=-185.1(0.00%) | Like=-175.29..-8.01 [-200.9572..-109.8084] | it/evals=1710/3511 eff=54.9662% N=400

Z=-180.2(0.00%) | Like=-170.97..-8.01 [-200.9572..-109.8084] | it/evals=1720/3525 eff=55.0400% N=400

Z=-167.1(0.00%) | Like=-157.88..-8.01 [-200.9572..-109.8084] | it/evals=1752/3571 eff=55.2507% N=400

Z=-165.1(0.00%) | Like=-155.98..-8.01 [-200.9572..-109.8084] | it/evals=1760/3581 eff=55.3285% N=400

Z=-153.4(0.00%) | Like=-144.22..-7.91 [-200.9572..-109.8084] | it/evals=1800/3638 eff=55.5899% N=400

Z=-143.0(0.00%) | Like=-132.79..-7.91 [-200.9572..-109.8084] | it/evals=1840/3698 eff=55.7914% N=400

Z=-129.4(0.00%) | Like=-120.34..-7.91 [-200.9572..-109.8084] | it/evals=1880/3764 eff=55.8859% N=400

Z=-126.5(0.00%) | Like=-117.20..-7.91 [-200.9572..-109.8084] | it/evals=1890/3781 eff=55.9006% N=400

Z=-119.1(0.00%) | Like=-109.69..-7.63 [-109.6935..-63.4188] | it/evals=1920/3818 eff=56.1732% N=400

Z=-112.1(0.00%) | Like=-102.89..-7.63 [-109.6935..-63.4188] | it/evals=1960/3871 eff=56.4679% N=400

Z=-108.0(0.00%) | Like=-98.89..-7.63 [-109.6935..-63.4188] | it/evals=1980/3900 eff=56.5714% N=400

Z=-102.8(0.00%) | Like=-93.24..-7.63 [-109.6935..-63.4188] | it/evals=2000/3929 eff=56.6733% N=400

Z=-94.5(0.00%) | Like=-85.18..-7.63 [-109.6935..-63.4188] | it/evals=2040/3983 eff=56.9355% N=400

Z=-89.0(0.00%) | Like=-79.71..-7.63 [-109.6935..-63.4188] | it/evals=2070/4018 eff=57.2139% N=400

Z=-87.5(0.00%) | Like=-77.75..-7.63 [-109.6935..-63.4188] | it/evals=2080/4031 eff=57.2845% N=400

Z=-81.8(0.00%) | Like=-72.12..-7.63 [-109.6935..-63.4188] | it/evals=2120/4084 eff=57.5461% N=400

Z=-76.0(0.00%) | Like=-66.57..-7.63 [-109.6935..-63.4188] | it/evals=2160/4149 eff=57.6154% N=400

Z=-70.9(0.00%) | Like=-61.50..-7.63 [-63.2849..-36.9287] | it/evals=2200/4200 eff=57.8947% N=400

Z=-66.4(0.00%) | Like=-57.09..-7.63 [-63.2849..-36.9287] | it/evals=2240/4255 eff=58.1064% N=400

Z=-65.6(0.00%) | Like=-56.41..-7.63 [-63.2849..-36.9287] | it/evals=2250/4267 eff=58.1846% N=400

Z=-63.1(0.00%) | Like=-53.43..-7.63 [-63.2849..-36.9287] | it/evals=2280/4304 eff=58.4016% N=400

Z=-57.9(0.00%) | Like=-48.38..-7.63 [-63.2849..-36.9287] | it/evals=2320/4363 eff=58.5415% N=400

Z=-56.1(0.00%) | Like=-46.84..-7.63 [-63.2849..-36.9287] | it/evals=2340/4400 eff=58.5000% N=400

Z=-54.7(0.00%) | Like=-45.21..-7.63 [-63.2849..-36.9287] | it/evals=2360/4428 eff=58.5899% N=400

Z=-50.9(0.00%) | Like=-41.02..-7.63 [-63.2849..-36.9287] | it/evals=2400/4482 eff=58.7947% N=400

Z=-48.0(0.00%) | Like=-38.78..-7.63 [-63.2849..-36.9287] | it/evals=2430/4529 eff=58.8520% N=400

Z=-47.4(0.00%) | Like=-38.01..-7.63 [-63.2849..-36.9287] | it/evals=2440/4540 eff=58.9372% N=400

Z=-44.4(0.00%) | Like=-34.74..-7.63 [-36.8890..-22.6112] | it/evals=2480/4598 eff=59.0758% N=400

Z=-42.3(0.00%) | Like=-32.60..-7.63 [-36.8890..-22.6112] | it/evals=2508/4641 eff=59.1370% N=400

Z=-41.3(0.00%) | Like=-31.61..-7.63 [-36.8890..-22.6112] | it/evals=2520/4655 eff=59.2244% N=400

Z=-39.0(0.00%) | Like=-29.27..-7.63 [-36.8890..-22.6112] | it/evals=2560/4712 eff=59.3692% N=400

Z=-36.7(0.00%) | Like=-27.12..-7.63 [-36.8890..-22.6112] | it/evals=2600/4773 eff=59.4558% N=400

Z=-36.2(0.00%) | Like=-26.58..-7.63 [-36.8890..-22.6112] | it/evals=2610/4787 eff=59.4940% N=400

Z=-34.7(0.00%) | Like=-25.23..-7.63 [-36.8890..-22.6112] | it/evals=2640/4822 eff=59.7015% N=400

Z=-33.3(0.00%) | Like=-24.17..-7.63 [-36.8890..-22.6112] | it/evals=2680/4868 eff=59.9821% N=400

Z=-32.7(0.00%) | Like=-23.37..-7.63 [-36.8890..-22.6112] | it/evals=2700/4894 eff=60.0801% N=400

Z=-32.1(0.00%) | Like=-22.64..-7.57 [-36.8890..-22.6112] | it/evals=2720/4919 eff=60.1903% N=400

Z=-30.9(0.00%) | Like=-21.61..-7.57 [-22.6029..-15.5287] | it/evals=2760/4973 eff=60.3543% N=400

Z=-30.2(0.00%) | Like=-20.78..-7.57 [-22.6029..-15.5287] | it/evals=2790/5012 eff=60.4944% N=400

Z=-29.9(0.00%) | Like=-20.30..-7.57 [-22.6029..-15.5287] | it/evals=2800/5028 eff=60.5013% N=400

Z=-28.8(0.00%) | Like=-19.32..-7.57 [-22.6029..-15.5287] | it/evals=2840/5081 eff=60.6708% N=400

Z=-27.6(0.00%) | Like=-18.13..-7.57 [-22.6029..-15.5287] | it/evals=2880/5132 eff=60.8622% N=400

Z=-26.7(0.01%) | Like=-17.11..-7.57 [-22.6029..-15.5287] | it/evals=2920/5177 eff=61.1262% N=400

Z=-25.8(0.01%) | Like=-16.37..-7.57 [-22.6029..-15.5287] | it/evals=2960/5230 eff=61.2836% N=400

Z=-25.6(0.02%) | Like=-16.11..-7.57 [-22.6029..-15.5287] | it/evals=2970/5241 eff=61.3510% N=400

Z=-25.0(0.03%) | Like=-15.36..-7.57 [-15.5249..-14.7766] | it/evals=2999/5280 eff=61.4549% N=400

Z=-25.0(0.03%) | Like=-15.36..-7.57 [-15.5249..-14.7766] | it/evals=3000/5281 eff=61.4628% N=400

Z=-24.2(0.08%) | Like=-14.53..-7.57 [-14.5252..-14.4775] | it/evals=3040/5330 eff=61.6633% N=400

Z=-23.8(0.11%) | Like=-14.22..-7.57 [-14.2182..-14.2021] | it/evals=3060/5355 eff=61.7558% N=400

Z=-23.5(0.15%) | Like=-13.78..-7.57 [-13.7752..-13.7746]*| it/evals=3080/5385 eff=61.7854% N=400

Z=-22.8(0.30%) | Like=-13.15..-7.57 [-13.1500..-13.1272] | it/evals=3120/5436 eff=61.9539% N=400

Z=-22.3(0.49%) | Like=-12.74..-7.57 [-12.7404..-12.7265] | it/evals=3150/5480 eff=62.0079% N=400

Z=-22.2(0.56%) | Like=-12.61..-7.57 [-12.6132..-12.6085]*| it/evals=3160/5493 eff=62.0459% N=400

Z=-21.7(0.96%) | Like=-12.05..-7.57 [-12.0462..-12.0455]*| it/evals=3200/5541 eff=62.2447% N=400

Z=-21.2(1.53%) | Like=-11.64..-7.53 [-11.6552..-11.6363] | it/evals=3240/5600 eff=62.3077% N=400

Z=-20.8(2.29%) | Like=-11.34..-7.53 [-11.3424..-11.3422]*| it/evals=3280/5648 eff=62.5000% N=400

Z=-20.5(3.19%) | Like=-11.02..-7.53 [-11.0166..-11.0057] | it/evals=3320/5702 eff=62.6179% N=400

Z=-20.4(3.41%) | Like=-10.90..-7.53 [-10.9049..-10.8983]*| it/evals=3330/5712 eff=62.6883% N=400

Z=-20.2(4.38%) | Like=-10.68..-7.53 [-10.6847..-10.6749]*| it/evals=3360/5749 eff=62.8155% N=400

Z=-19.9(5.84%) | Like=-10.42..-7.53 [-10.4187..-10.4172]*| it/evals=3400/5807 eff=62.8814% N=400

Z=-19.8(6.66%) | Like=-10.29..-7.53 [-10.2898..-10.2873]*| it/evals=3420/5843 eff=62.8330% N=400

Z=-19.7(7.35%) | Like=-10.20..-7.53 [-10.1978..-10.1972]*| it/evals=3435/5860 eff=62.9121% N=400

Z=-19.6(7.60%) | Like=-10.18..-7.53 [-10.1809..-10.1716]*| it/evals=3440/5866 eff=62.9345% N=400

Z=-19.4(9.62%) | Like=-9.95..-7.53 [-9.9475..-9.9467]*| it/evals=3480/5916 eff=63.0892% N=400

Z=-19.3(11.20%) | Like=-9.74..-7.53 [-9.7355..-9.7270]*| it/evals=3510/5955 eff=63.1863% N=400

Z=-19.2(11.87%) | Like=-9.70..-7.53 [-9.6990..-9.6943]*| it/evals=3520/5965 eff=63.2525% N=400

Z=-19.0(14.54%) | Like=-9.42..-7.53 [-9.4219..-9.4202]*| it/evals=3560/6012 eff=63.4355% N=400

Z=-18.8(17.57%) | Like=-9.25..-7.53 [-9.2519..-9.2422]*| it/evals=3600/6067 eff=63.5257% N=400

Z=-18.7(21.01%) | Like=-9.09..-7.53 [-9.0896..-9.0887]*| it/evals=3640/6121 eff=63.6252% N=400

Z=-18.5(24.29%) | Like=-8.96..-7.53 [-8.9632..-8.9631]*| it/evals=3680/6185 eff=63.6128% N=400

Z=-18.5(25.21%) | Like=-8.94..-7.53 [-8.9448..-8.9419]*| it/evals=3690/6196 eff=63.6646% N=400

Z=-18.4(27.62%) | Like=-8.86..-7.53 [-8.8556..-8.8513]*| it/evals=3720/6233 eff=63.7751% N=400

Z=-18.3(31.04%) | Like=-8.70..-7.53 [-8.7034..-8.7028]*| it/evals=3760/6287 eff=63.8695% N=400

Z=-18.2(32.84%) | Like=-8.68..-7.53 [-8.6815..-8.6738]*| it/evals=3780/6314 eff=63.9161% N=400

Z=-18.1(34.67%) | Like=-8.62..-7.53 [-8.6189..-8.6138]*| it/evals=3800/6337 eff=64.0054% N=400

Z=-18.0(38.19%) | Like=-8.50..-7.53 [-8.4997..-8.4972]*| it/evals=3840/6387 eff=64.1390% N=400

Z=-18.0(40.99%) | Like=-8.40..-7.53 [-8.3981..-8.3951]*| it/evals=3870/6434 eff=64.1366% N=400

Z=-18.0(41.96%) | Like=-8.37..-7.53 [-8.3722..-8.3722]*| it/evals=3880/6446 eff=64.1747% N=400

Z=-17.9(45.53%) | Like=-8.30..-7.53 [-8.3041..-8.3030]*| it/evals=3920/6498 eff=64.2834% N=400

Z=-17.8(49.17%) | Like=-8.23..-7.53 [-8.2267..-8.2259]*| it/evals=3960/6571 eff=64.1711% N=400

[ultranest] Explored until L=-8

[ultranest] Likelihood function evaluations: 6580

[ultranest]   logZ = -17.05 +- 0.1237

[ultranest] Effective samples strategy satisfied (ESS = 983.9, need >400)

[ultranest] Posterior uncertainty strategy is satisfied (KL: 0.46+-0.06 nat, need <0.50 nat)

[ultranest] Evidency uncertainty strategy is satisfied (dlogz=0.42, need <0.5)

[ultranest]   logZ error budget: single: 0.15 bs:0.12 tail:0.41 total:0.42 required:<0.50

[ultranest] done iterating.

18:26:35 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	1.016 +/- 0.015	1 / (cm2 keV s)
demo.spectrum.main.Sin.f	(9.96 -0.05 +0.06) x 10^-2	rad / keV

Values of -log(posterior) at the minimum:

	-log(posterior)
demo	-7.545849
total	-7.545849

Values of statistical measures:

	statistical measures
AIC	19.797580
BIC	21.083162
DIC	19.134711
PDIC	2.025942
log(Z)	-7.419405

[10]:

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