Abstract
Sherpa is a generalized modeling and fitting package. Primarily developed for the Chandra Interactive Analysis of Observations (CIAO) package by the Chandra X-ray Center, Sherpa provides an Object-Oriented Programming (OOP) API for parametric data modeling. It is designed to use the forward fitting technique to search for the set of best-fit parameter values in parametrized model functions. Sherpa can also estimate the confidence limits on best-fit parameters using a new confidence method or using an algorithm based on Markov chain Monte Carlo (MCMC). Confidence limits on parameter values are necessary for any data analysis result, but can be non-trivial to compute in a non-linear and multi-parameter space. This new, robust confidence method can estimate confidence limits of Sherpa parameters using a finite convergence rate. The Sherpa extension module, pyBLoCXS, implements a sophisticated Bayesian MCMC-based algorithm for simple single-component spectral mod- els defined in Sherpa. pyBLoCXS has primarily been developed in Python using high-energy X-ray spectral data. We describe the algorithm including the features for defining priors and incorporating deviations in the calibration information. We will demonstrate examples of estimating confidence limits using the confidence method and processing simulations using pyBLoCXS. Index Terms—modeling, fitting, parameter, confidence, mcmc, bayesian
Highlights
IntroductionGeneral purpose modeling and fitting application written in Python and Python C/C++/FORTRAN extensions
Sherpa is an extensible, general purpose modeling and fitting application written in Python and Python C/C++/FORTRAN extensions
We describe several methods we make available to Sherpa users and Python programmers to put confidence limits on fitted parameter values
Summary
General purpose modeling and fitting application written in Python and Python C/C++/FORTRAN extensions. If the user can examine this probability distribution in some way, the user can determine how well the best-fit parameter values are constrained Such constraints are often summarized as confidence limits, stating that parameters are known to a certain level of confidence [avn1976]. After an examination of parameter space, the user might determine that, for a model having temperature as a parameter, a best-fit temperature of 1.2 keV has 90% confidence limits of +0.2 keV, -0.4 keV. We discuss a confidence limit function included in Sherpa, that examines parameter space near the local minimum representing best-fit parameter values, and that returns the desired confidence limits. We present a new Python module providing a Bayesian approach to deriving fitted parameter values and confidence limits: pyBLoCXS, a new importable Python module, that allows use of prior distributions on model parameters via extensions to Sherpa statistics classes. Where p(θ |d, I) represents the posterior distribution; p(d|θ , I), the likelihood; p(θ |I), the prior; and p(d|I) is considered constant
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