Exact and Approximate Markov Chain Sampling Algorithms

University Of Florida, Gainesville FL

Investigators

Abstract

ABSTRACT Prop ID: DMS-0503648 PI: Hobert, James P. NSF Program: STATISTICS Institution: University of Florida Title: Exact and Approximate Markov Chain Sampling Algorithms The disadvantages of Markov chain Monte Carlo (MCMC) methods (relative to classical Monte Carlo techniques) can sometimes be overcome via perfect sampling, which is a method of converting the underlying Markov chain into an algorithm that produces independent and identically distributed samples from its stationary distribution. Unfortunately, perfect sampling algorithms have not lived up to their expectations for handling intractable distributions whose support is unbounded and continuous. The investigator develops a wide-ranging perfect sampling algorithm that is particularly well-suited to such distributions. The basic idea is to exploit a mixture representation of the a stationary distribution. The investigator also studies techniques for Bayesian analysis of the market model, which is a multivariate regression model used by financial economists to analyze data on asset returns. Empirical evidence and theoretical arguments suggest that the errors in this model should be from a heavy-tailed, elliptically symmetric distribution. However, the Bayesian methodology that has been developed for making inferences via the market model is based on the assumption of multivariate normal errors. This disconnect is presumably due to the fact that the posterior distributions corresponding to the heavy-tailed alternatives are highly intractable. The PI develops and analyzes Monte Carlo and MCMC methods for exploring such posterior distributions. Bayesian statistical methods of analyzing data often require the user to deal with intractable probability distributions. The investigator develops sampling algorithms that facilitate the use of such Bayesian methods. These algorithms enhance infrastructure for research and education by providing scientists from many different disciplines with better techniques for making inferences from their data. ----------------------------------------------------------------------