Benchmark Estimation for Markov Chain Monte Carlo Samples

Description

Benchmark Estimation for Markov Chain Monte Carlo Samples
Subharup Guha, Steven N. MacEachern and Mario Peruggia
[e-mail]
May 2002; revised November 2002
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 and provide
a theoretical basis for the method. The methodology and beneflts 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 and show that greater beneflts accrue with
the thinner subsamples that are often used in practice.
1 Introduction
While using an MCMC sample to investigate the posterior distribution of a vector-valued parameter ,
many features of interest have the representation E[g( )] for some function g( ). A subsample of
the MCMC output is often all that is retained for further investigation of the posterior distribution.
Subsamplingisoftennecessaryincomputationallyintensiveorreal-time,interactiveinvestigationswhere
speed is essential. Examples include expensive plot processing and examination of changes in the prior
(sensitivity analysis), likelihood (robustness) or data (case in uence). ...

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• Published by: Phoem
• Reads: 42
• Language: English