Bayesian Estimation of LogN-LogS with Nonignorable Missing Data

• Activity Number: 225
• Type: Topic Contributed
• Date/Time: Monday, July 30, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Paul Baines*+ and Irina Udaltsova
• Companies: University of California at Davis and University of California at Davis
• Keywords: Bayesian Inference ; Astrostatistics ; Missing Data ; MCMC ; Model Checking

Abstract

The study of astrophysical source populations is often conducted using the cumulative distribution of the number of sources detected at a given sensitivity. The resulting "log(N>S)-logS" relationship can be used to compare and evaluate theoretical models for source populations and their evolution. In practice, however, inferring properties of source populations from observational data is complicated by detector-induced uncertainties, background contamination and missing data. Since the probability of a non-detected source is a function of the unobserved source intensity, the missing data mechanism is non-ignorable. By investigating the connection between probabilistic and theoretical assumptions in commonly used logN-logS methods, we propose a new class of models with a more realistic physical interpretation. Our Bayesian approach leads to computationally efficient inference for physical model parameters and the corrected log(N>S)-log(S) distribution for source populations. Our method extends existing work in allowing for both non-ignorable missing data and an unknown number of unobserved sources. We conclude with some novel multivariate strategies for Bayesian model checking.