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Fitting and Estimating Parameter Confidence Limits with Sherpa

Brian Refsdal
Smithsonian Astrophysical Observatory

Stephen Doe
Smithsonian Astrophysical Observatory

Dan Nguyen
Smithsonian Astrophysical Observatory

Aneta Siemiginowska
Smithsonian Astrophysical Observatory

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 models 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.

Keywords

modeling, fitting, parameter, confidence, mcmc, bayesian

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