Benchmark Estimation for Markov Chain Monte Carlo Samples

• Activity Number: 201
• Type: Topic Contributed
• Date/Time: Tuesday, August 13, 2002 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Graphics*
• Author(s): Subharup Guha*+ and Steven MacEachern and Mario Peruggia
• Affiliation(s): Ohio State University and Ohio State University and Ohio State University
• Keywords: variance reduction ; subsample ; maximum entropy ; stratification

Abstract

While studying various features of the posterior distribution of a vector-valued parameter using an MCMC sample, a subsample is often all that is available for analysis. The goal of benchmark estimation is to use the best available information--i.e., the full MCMC sample, to improve future estimates made on the basis of the subsample. We discuss a simple approach to do this. The methodology and benefits of benchmark estimation are illustrated using a well-known example from the literature. We obtain as much as an 80% reduction in MSE with the technique based on a 1-in-10 subsample. Greater benefits accrue with the thinner subsamples often used in practice. Further motivation, results, and investigations will be discussed.