get_draws

sherpa.astro.ui.get_draws(id=None, otherids=(), niter=1000, covar_matrix=None)

Run the pyBLoCXS MCMC algorithm.

The function runs a Markov Chain Monte Carlo (MCMC) algorithm designed to carry out Bayesian Low-Count X-ray Spectral (BLoCXS) analysis. It explores the model parameter space at the suspected statistic minimum (i.e. after using fit). The return values include the statistic value, parameter values, and an acceptance flag indicating whether the row represents a jump from the current location or not. For more information see the sherpa.sim module and 1.

Parameters
  • id (int or str, optional) – The data set containing the data and model. If not given then the default identifier is used, as returned by get_default_id.

  • otherids (sequence of int or str, optional) – Other data sets to use in the calculation.

  • niter (int, optional) – The number of draws to use. The default is 1000.

  • covar_matrix (2D array, optional) – The covariance matrix to use. If None then the result from get_covar_results().extra_output is used.

Returns

The results of the MCMC chain. The stats and accept arrays contain niter+1 elements, with the first row being the starting values. The params array has (nparams, niter+1) elements, where nparams is the number of free parameters in the model expression, and the first column contains the values that the chain starts at. The accept array contains boolean values, indicating whether the jump, or step, was accepted (True), so the parameter values and statistic change, or it wasn’t, in which case there is no change to the previous row. The sherpa.utils.get_error_estimates routine can be used to calculate the credible one-sigma interval from the params array.

Return type

stats, accept, params

See also

covar()

Estimate the confidence intervals using the covariance method.

fit()

Fit a model to one or more data sets.

plot_cdf()

Plot the cumulative density function of an array.

plot_pdf()

Plot the probability density function of an array.

plot_scatter()

Create a scatter plot.

plot_trace()

Create a trace plot of row number versus value.

set_prior()

Set the prior function to use with a parameter.

set_sampler()

Set the MCMC sampler.

get_sampler()

Return information about the current MCMC sampler.

Notes

The chain is run using fit information associated with the specified data set, or sets, the currently set sampler (set_sampler) and parameter priors (set_prior), for a specified number of iterations. The model should have been fit to find the best-fit parameters, and covar called, before running get_draws. The results from get_draws is used to estimate the parameter distributions.

References

1

“Analysis of Energy Spectra with Low Photon Counts via Bayesian Posterior Simulation”, van Dyk, D.A., Connors, A., Kashyap, V.L., & Siemiginowska, A. 2001, Ap.J., 548, 224 http://adsabs.harvard.edu/abs/2001ApJ…548..224V

Examples

Fit a source and then run a chain to investigate the parameter distributions. The distribution of the stats values created by the chain is then displayed, using plot_trace, and the parameter distributions for the first two thawed parameters are displayed. The first one as a cumulative distribution using plot_cdf and the second one as a probability distribution using plot_pdf. Finally the acceptance fraction (number of draws where the chain moved) is displayed. Note that in a full analysis session a burn-in period would normally be removed from the chain before using the results.

>>> fit()
>>> covar()
>>> stats, accept, params = get_draws(1, niter=1e4)
>>> plot_trace(stats, name='stat')
>>> names = [p.fullname for p in get_source().pars if not p.frozen]
>>> plot_cdf(params[0,:], name=names[0], xlabel=names[0])
>>> plot_pdf(params[1,:], name=names[1], xlabel=names[1])
>>> accept[:-1].sum() * 1.0 / len(accept - 1)
0.4287

The following runs the chain on multiple data sets, with identifiers ‘core’, ‘jet1’, and ‘jet2’:

>>> stats, accept, params = get_draws('core', ['jet1', 'jet2'], niter=1e4)