Abstract #300998

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JSM 2003 Abstract #300998
Activity Number: 208
Type: Contributed
Date/Time: Tuesday, August 5, 2003 : 8:30 AM to 10:20 AM
Sponsor: Section on Statistical Computing
Abstract - #300998
Title: Reversible Jump MCMC By Example
Author(s): Patrick J. Gaffney*+
Companies: The Lubrizol Corporation
Address: 29400 Lakeland Blvd., Drop 152A, Wickliffe, OH, 44092,
Keywords: reversible jump ; MCMC ; Bayesian ; harmonic mean estimator ; sensitivity ; burn-in
Abstract:

This paper applies reversible jump MCMC to linear regression models. This problem can be addressed using Bayesian variable assessment, a MCMC-based approach, and so is an ideal system to investigate different choices for the birth-death proposal distribution. In Bayesian analysis, sensitivity to the prior is an important issue. Thus the effect of different choices for the prior is examined, in particular the prior for the effects. Understanding how the birth-death acceptance ratio is formed can sometimes be challenging. The linear regression model is a useful system to show that the birth-death step is correct. A more general approach to verify correctness of the ratio, using the harmonic mean estimator, is outlined. Initializing the chain is ignored in many publications. In practice, some use standard frequentist techniques. An alternative way of initializing any RJ-MCMC chain, termed pre-burn-in, is introduced. The prior for the number of terms is set to a high value for a short pre-burn-in period, resulting in the rapid inclusion of many terms in the model. Thus one can begin the pre-burn-in phase using a very simple model, e.g., one with only a constant term.

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