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

Abstract

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 χ 2 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 χ 2 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 χ 2 method than in Poisson statistics. Here, this is a consequence of the uncertainties being dominated by counting statistics, and therefore highlights the need to choose the appropriate fit statistic.

Authors:
 [1];  [2];  [1];  [1];  [1];  [3]; ORCiD logo [3];  [3];  [3];  [4];  [5]
  1. Tokyo Metropolitan Univ., Tokyo (Japan)
  2. Tokyo Metropolitan Univ., Tokyo (Japan); KTH Royal Inst. of Technology, Stockholm (Sweden)
  3. NASA Goddard Space Flight Center, Greenbelt, MD (United States)
  4. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  5. Yale Univ., New Haven, CT (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1560117
Alternate Identifier(s):
OSTI ID: 1560881
Report Number(s):
LLNL-JRNL-771761
Journal ID: ISSN 0004-6264; 963384
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Accepted Manuscript
Journal Name:
Publications of the Astronomical Society of Japan
Additional Journal Information:
Journal Volume: 71; Journal Issue: 4; Journal ID: ISSN 0004-6264
Publisher:
Astronomical Society of Japan
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS

Citation Formats

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., and Szymkowiak, Andrew. Poisson vs. Gaussian statistics for sparse X-ray data: Application to the soft X-ray spectrometer. United States: N. p., 2019. Web. doi:10.1093/pasj/psz053.
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. Poisson vs. Gaussian statistics for sparse X-ray data: Application to the soft X-ray spectrometer. United States. doi:10.1093/pasj/psz053.
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., and Szymkowiak, Andrew. Fri . "Poisson vs. Gaussian statistics for sparse X-ray data: Application to the soft X-ray spectrometer". United States. doi:10.1093/pasj/psz053.
@article{osti_1560117,
title = {Poisson vs. Gaussian statistics for sparse X-ray data: Application to the soft X-ray spectrometer},
author = {Yamada, Shinya and Axelsson, Magnus and Ishisaki, Yoshitaka and Konami, Saori and Takemura, Nozomi and Kelley, Richard L. and Kilbourne, Caroline A. and Leutenegger, Maurice A. and Porter, F. Scott and Eckart, Megan E. and Szymkowiak, Andrew},
abstractNote = {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. Here, this is a consequence of the uncertainties being dominated by counting statistics, and therefore highlights the need to choose the appropriate fit statistic.},
doi = {10.1093/pasj/psz053},
journal = {Publications of the Astronomical Society of Japan},
number = 4,
volume = 71,
place = {United States},
year = {2019},
month = {7}
}

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