Bayesian Mixture Modeling and Model Misspecification for Astrophysical Populations

• Activity Number: 136
• Type: Contributed
• Date/Time: Monday, July 30, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Irina Udaltsova*+ and Paul Baines
• Companies: University of California at Davis and University of California at Davis
• Keywords: Bayesian Modeling ; Model Misspecification ; Mixture Modeling ; Astrostatistics

Abstract

For a number of estimation problems in cosmology, Bayesian methods is a natural choice, because they incorporate prior knowledge about a measurement and help reduce bias in estimation by correctly accounting for non-ignorable missing data. In this talk we present the Bayesian methodology for studying source populations, such as X-ray pulsars, with the estimation of log(N) - log(S) curve, a cumulative distribution of the number of sources (N) detected at a given sensitivity (S). We describe a new hierarchical Bayesian model in the presence of non-ignorable missing data to estimate the boundary parameters, or "break-points", for the mixture model in addition to other estimated parameters. This work is an extension of the method estimating a straight log(N) - log(S) relationship jointly with the flux of observed sources and the number of sources unobserved due to detector effects, and it enables model flexibility to represent the population in a more physically meaningful way. We present a thorough study of the behavior of our model with a misspecified number of mixture components.