Effective MCMC for Over-Dispersed Models

• Activity Number: 366
• Type: Contributed
• Date/Time: Wednesday, August 6, 2003 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Stat. Sciences
• Author(s): Subharup Guha*+ and Steven N. MacEachern and Mario Peruggia
• Companies: The Ohio State University and Ohio State University and The Ohio State University
• Keywords: benchmark estimation ; importance sampling ; variance reduction

Abstract

While investigating the posterior distribution of a vector-valued parameter, interest often focuses on whether an over- or underdispersed model belonging to a class provides a good fit to the observed data. If the set of models includes one with a conjugate hierarchical structure, of-the-shelf software like BUGS can be used to easily generate MCMC draws from the posterior. A systematic subsample of draws is often all that is retained for analysis due to the intensive computations involved. Based on this stored subsample, the Bayes factor of each model in the class can be estimated and the "best-fitting" model found. Various features of its posterior can be estimated by importance sampling. Importance link function transformations provide a way to stabilize the importance sampling weights when the best-fitting model corresponds to substantial overdispersion. Further reductions in variability are achieved by the technique of benchmark estimation. We illustrate this methodology using a well-known example from the literature. We also verify the accuracy of expressions for the asymptotic reductions in variance achieved by benchmark-weighted importance sampling estimators.