Optimization Methods in Sherpa

Details Optimization Methods in Sherpa Optimization Methods in Sherpa

Sep 2009

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009cfdd.confe.196s&link_type=abstract

Chandra's First Decade of Discovery, Proceedings of the conference held 22-25 September, 2009 in Boston, MA. Edited by Scott Wo

Astronomy and Astrophysics

Astronomy

Source Catalogs, Software

Scientific paper

Forward fitting is a standard technique used to model X-ray data. A statistic, usually assumed weighted chi^2 or Poisson likelihood (e.g. Cash), is minimized in the fitting process to obtain a set of the best model parameters. Astronomical models often have complex forms with many parameters that can be correlated (e.g. an absorbed power law). Minimization is not trivial in such setting, as the statistical parameter space becomes multimodal and finding the global minimum is hard. Standard minimization algorithms can be found in many libraries of scientific functions, but they are usually focused on specific functions. However, Sherpa designed as general fitting and modeling application requires very robust optimization methods that can be applied to variety of astronomical data (X-ray spectra, images, timing, optical data etc.). We developed several optimization algorithms in Sherpa targeting a wide range of minimization problems. Two local minimization methods were built: Levenberg-Marquardt algorithm was obtained from MINPACK subroutine LMDIF and modified to achieve the required robustness; and Nelder-Mead simplex method has been implemented in-house based on variations of the algorithm described in the literature. A global search Monte-Carlo method has been implemented following a differential evolution algorithm presented by Storn and Price (1997). We will present the methods in Sherpa and discuss their usage cases. We will focus on the application to Chandra data showing both 1D and 2D examples. This work is supported by NASA contract NAS8-03060 (CXC).

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