Abstract

In the first half of the talk, a statistical framework for obtaining proper concordance among different instruments measuring the same set of astronomical sources will be presented. Calibration data are often obtained by observing several well-understood objects simultaneously with multiple instruments, such as satellites for measuring astronomical sources. Analyzing such data and obtaining proper concordance among the instruments is challenging when the physical source models are not well understood, when there are uncertainties in “known” physical quantities, or when data quality varies in ways that cannot be fully quantified. We propose a log-Normal model and a more general log-t model that respect the multiplicative nature of the mean signals via a half-variance adjustment, yet permit imperfections in the mean modeling to be absorbed by residual variances. In the second half of the talk, a formal statistical analysis of both the theoretical properties and computational algorithms for the c-stat aka Cash-stat, a quantity for model fitting and goodness-of-fit assessment widely adopted by astronomers, will be presented. Recommendations of practical procedures will be given based on numerical experiments.