Accounting for calibration uncertainties in X-ray analysis: Effective areas in spectral fitting

Hyunsook Lee, Vinay L. Kashyap, David A. Van Dyk, Alanna Connors, Jeremy J. Drake, Rima Izem, Xiao Li Meng, Shandong Min, Taeyoung Park, Pete Ratzlaff, Aneta Siemiginowska, Andreas Zezas

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Abstract

While considerable advance has been made to account for statistical uncertainties in astronomical analyses, systematic instrumental uncertainties have been generally ignored. This can be crucial to a proper interpretation of analysis results because instrumental calibration uncertainty is a form of systematic uncertainty. Ignoring it can underestimate error bars and introduce bias into the fitted values of model parameters. Accounting for such uncertainties currently requires extensive case-specific simulations if using existing analysis packages. Here, we present general statistical methods that incorporate calibration uncertainties into spectral analysis of high-energy data. We first present a method based on multiple imputation that can be applied with any fitting method, but is necessarily approximate. We then describe a more exact Bayesian approach that works in conjunction with a Markov chain Monte Carlo based fitting. We explore methods for improving computational efficiency, and in particular detail a method of summarizing calibration uncertainties with a principal component analysis of samples of plausible calibration files. This method is implemented using recently codified Chandra effective area uncertainties for low-resolution spectral analysis and is verified using both simulated and actual Chandra data. Our procedure for incorporating effective area uncertainty is easily generalized to other types of calibration uncertainties.

Original languageEnglish
Article number126
JournalAstrophysical Journal
Volume731
Issue number2
DOIs
Publication statusPublished - 2011 Apr 20

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All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science

Cite this

Lee, H., Kashyap, V. L., Van Dyk, D. A., Connors, A., Drake, J. J., Izem, R., Meng, X. L., Min, S., Park, T., Ratzlaff, P., Siemiginowska, A., & Zezas, A. (2011). Accounting for calibration uncertainties in X-ray analysis: Effective areas in spectral fitting. Astrophysical Journal, 731(2), [126]. https://doi.org/10.1088/0004-637X/731/2/126