A new MCMC module for Bayesian Spectral Analysis in Sherpa

Statistics – Computation

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Standard statistical methods for addressing parameter uncertainty may not always be appropriate for sophisticated spectral models. Typically relying on high-count approximations, standard methods applied to low-count data may result in misleading error bars. For example, when fitting a narrow emission line, there may be several separate likely values for its location that cannot be summarized with simple error bars. Finding possible locations requires sophisticated techniques capable of exploring the sometimes highly multi-modal posterior distribution, while testing for the presence of a line requires computational methods such as PPP (Protassov et al 2002) since standard p-values do not apply. Methods that fully explore the parameter space, such as MCMC, provide a more complete picture of parameter uncertainty. The use of MCMC for Bayesian analysis of spectral models has been explored and validated, (van Dyk et al 2004, 2006; Park, van Dyk, and Siemiginowska 2008), but up until now has required specialized software that could only accommodate a specific class of models. We are in the process of developing a new, more flexible computational module that will allow these techniques to be used with most models available in Sherpa. The computational module has been validated for a class of background-contaminated absorbed single-component models including power law, blackbody, and thermal bremsstrahlung. Statistically, our MCMC method relies on default non-informative prior distributions that do not need to be specified by the user. For computational and statistical reasons, we use normalizing transformations of the parameters, though estimates and confidence intervals are provided on the standard physical scale. For more complex models, more sophisticated techniques will have to be employed. Multiple modes may require techniques such as simulated annealing or MH with multiple proposal distributions. For samplers with high rejection rates due to strong posterior correlations, we will explore Metropolis within Gibbs using dynamic correlation reduction.

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