Reference Priors for Constrained Poisson Models

• Activity Number: 349
• Type: Contributed
• Date/Time: Tuesday, August 3, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Michael David Sonksen*+ and Mario Peruggia
• Companies: The Ohio State University and The Ohio State University
• Keywords: convexity ; monotonicity ; lung cancer rates ; mortality rates ; non-informative priors

Abstract

We construct reference priors for constrained Poisson models using the sequential algorithm of Berger and Bernardo (1992). The event counts for various groups of subjects are modeled as Poisson random variables with group specific rates. We consider situations in which the groups can be completely ordered according to one covariate or partially ordered according to two. In both cases the priors enforce monotonicity of the rates with respect to the ordering. For the case of a complete ordering we also develop priors that enforce an additional convexity constraint. We model a data set on mortality rates for men in different age groups assuming that the death rates are ordered with respect to age. We also model a data set on the incidence of lung cancer in men assuming that the cancer rates are partially ordered with respect to years of smoking and number of cigarettes smoked daily.