Abstract #301290

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JSM 2003 Abstract #301290
Activity Number: 419
Type: Contributed
Date/Time: Wednesday, August 6, 2003 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistical Computing
Abstract - #301290
Title: Multivariate Estimation via Markov Chain Monte Carlo
Author(s): Galin L. Jones*+
Companies: University of Minnesota
Address: School of Statistics, Minneapolis, MN, 55455,
Keywords: Markov chain ; Monte Carlo ; regeneration ; central limit theorem ; multivariate
Abstract:

A topic that has received surprisingly little attention in the Markov chain Monte Carlo (MCMC) literature is how to go about multivariate estimation. That is, suppose that the goal of the simulation is to estimate the expectation of a multivariate function with respect to some complicated target distribution. It has become common to use MCMC to form ergodic averages which accomplish this. However, there has been little discussion of how to calculate an appropriate Monte Carlo error. Here a multivariate central limit theorem is developed and two methods for estimating the asymptotic covariance matrix are presented. These methods will be illustrated and compared in the context of an example.

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