Bayesian Analysis of The Additive Mixed Model for Randomized Block Designs

• Activity Number: 46
• Type: Contributed
• Date/Time: Sunday, August 11, 2002 : 4:00 PM to 5:50 PM
• Sponsor: General Methodology
• Author(s): Jenting Wang*+ and John Hsu
• Affiliation(s): State University of New York, Oneonta and University of California, Santa Barbara
• Keywords: Laplacian approximation ; Monte Carlo simulation

Abstract

We consider an analysis of the randomized block design, with "b" blocks, to compare "t" treatments. The "t" treatments are randomly assigned to the experimental units within each block. The primary goal of the analysis is to compare the treatments. Suppose that some prior information about the treatments is available; hence, a Bayesian approach is to be taken. Let \theta_{i} be the mean for the "i" treatment. The parameter of interest for the analysis, \eta = g(\theta_{1}, \theta_{2}, \ldots, \theta_{t}, is a linear or nonlinear function of \theta_{1}, \theta_{2}, \ldots, \theta_{t}. The usual computation of the posterior density of \eta becomes tedious and imprecise when many treatments are involved. The posterior density of \eta, can be simulated from a multivariate-t distribution along with the use of the rejection method. An alternative Laplacian approximation, which produces a smooth density curve and only takes seconds of computation time, is also proposed. The approximation and simulation are both applied to an example of an iron absorption experiment, and a complete Bayesian analysis is reported.