Poisson vs. Gaussian statistics for sparse X-ray data: Application to the soft X-ray spectrometer

Yamada, Shinya; Axelsson, Magnus; Ishisaki, Yoshitaka; Konami, Saori; Takemura, Nozomi; Kelley, Richard L.; Kilbourne, Caroline A.; Leutenegger, Maurice A.; Porter, F. Scott; Eckart, Megan E.; Szymkowiak, Andrew

doi:10.1093/pasj/psz053

Poisson vs. Gaussian statistics for sparse X-ray data: Application to the soft X-ray spectrometer

Journal Article · Fri Jul 19 00:00:00 EDT 2019 · Publications of the Astronomical Society of Japan

DOI:https://doi.org/10.1093/pasj/psz053· OSTI ID:1560881

Yamada, Shinya; Axelsson, Magnus; Ishisaki, Yoshitaka; Konami, Saori; Takemura, Nozomi; Kelley, Richard L.; ; Leutenegger, Maurice A.; Porter, F. Scott; Eckart, Megan E.; Szymkowiak, Andrew

Abstract

Reliable results when fitting X-ray data require proper consideration of the statistics involved. We probe the impact of Gaussian versus Poisson statistics at low count levels using both the standard χ2 method and maximum likelihood based on Poisson (C) statistics. The difference is studied and quantified through simulated spectra with known properties. We then test the results through analysis of Mn Kα calibration data taken with the flight spare microcalorimeter for the Hitomi soft X-ray spectrometer. Through comparison with simulations, our results show that the χ2 method tends to give overly optimistic estimates of the detector energy resolution, in particular when there are few counts. Given an energy resolution of ∼5 eV and a line with about 100 photons, the line width becomes ∼10% lower in the χ2 method than in Poisson statistics. This is a consequence of the uncertainties being dominated by counting statistics, and therefore highlights the need to choose the appropriate fit statistic.

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Sponsoring Organization:: USDOE

OSTI ID:: 1560881

Journal Information:: Publications of the Astronomical Society of Japan, Journal Name: Publications of the Astronomical Society of Japan Journal Issue: 4 Vol. 71; ISSN 0004-6264

Publisher:: Oxford University PressCopyright Statement

Country of Publication:: Japan

Language:: English

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