IngentaConnect Nonconjugate Bayesian Analysis of Variance Component Models

Authors: Wolfinger, Russell D.¹; Kass, Robert E.²

Source: Biometrics, Volume 56, Number 3, September 2000 , pp. 768-774(7)

Abstract:

Summary.

We consider the usual normal linear mixed model for variance components from a Bayesian viewpoint. With conjugate priors and balanced data, Gibbs sampling is easy to implement; however, simulating from full conditionals can become difficult for the analysis of unbalanced data with possibly nonconjugate priors, thus leading one to consider alternative Markov chain Monte Carlo schemes. We propose and investigate a method for posterior simulation based on an independence chain. The method is customized to exploit the structure of the variance component model, and it works with arbitrary prior distributions. As a default reference prior, we use a version of Jeffreys' prior based on the integrated (restricted) likelihood. We demonstrate the ease of application and flexibility of this approach in familiar settings involving both balanced and unbalanced data.

Keywords: Independence chain; Jeffreys' prior; Mixed model; Posterior simulation; Reference prior; REML

Document Type: Research article

DOI: 10.1111/j.0006-341X.2000.00768.x

Affiliations: 1: SAS Institute, Inc., SAS Campus Drive, Gary, North Carolina 27513, U.S.A., Email: russ.wolfinger@sas.com 2: Department of Statistics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, U.S.A., Email: kass@stat.cmu.edu

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