Calibration with Multiplicative Means but Additive Errors: A Log Normal Approach

• Activity Number: 110
• Type: Topic Contributed
• Date/Time: Monday, August 1, 2016 : 8:30 AM to 10:20 AM
• Sponsor: Astrostatistics Special Interest Group
• Author(s): Yang Chen* and Xufei Wang and Xiao-Li Meng and Herman Marshall and David A. van Dyk and Matteo Guainazzi and Paul Plucinsky and Vinay Kashyap
• Companies: Harvard and Harvard and Harvard and MIT and Imperial College London and JAXA and CXC/CfA and Harvard
• Keywords: adjusting attributes ; shrinkage estimator ; Bayesian hierarchical model ; log-normal model ; half-variance adjustment

Abstract

Useful information to calibrate instruments used for astrophysical measurements is usually obtained by observing different sources with well-understood characteristics simultaneously with different detectors. This requires a careful modeling of the mean signals, the intrinsic source variations, and measurement errors. Because our data are typically large (>>30) photon counts, we propose an approximate log-normal model, with the advantage of permitting imperfection in the multiplicative mean model to be captured by the residual variance. The calibration takes an analytically tractable form of power shrinkage, with a half-variance adjustment to ensure an unbiased multiplicative mean model on the original scale. We also discuss its comparison with the (almost) exact Poisson model, which is much harder to accommodate model imperfection in the mean because its variance is restricted by the mean. These issues will be demonstrated via data from a combination of observations of AGNs and spectral line emission from the supernova remnant E0102, obtained with a variety of X-ray telescopes like Chandra, XMM-Newton, Suzaku, Swift, etc. The data are compiled by IACHEC researchers.