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A MCMC Algorithm to Fit a General Exchangeable Model

Summary: A MCMC Algorithm to Fit a General
Exchangeable Model
Jim Albert \Lambda
Bowling Green State University
and Duke University
September, 1994
Consider the exchangeable Bayesian hierarchical model where observations y i
are in­
dependently distributed from sampling densities with unknown means, the means ¯ i
a random sample from a distribution g, and the parameters of g are assigned a known
distribution h. A simple algorithm is presented for summarizing the posterior distri­
bution based on Gibbs sampling and the Metropolis algorithm. The software program
Matlab is used to implement the algorithm and provide a graphical output analysis. An
binomial example is used to illustrate the flexibility of modeling possible using this al­
gorithm. Methods of model checking and extensions to hierarchical regression modeling
are discussed.
1 Introduction
This article proposes a simple computational algorithm to summarize a general exchangeable


Source: Albert, James H. - Department of Mathematics and Statistics, Bowling Green State University


Collections: Mathematics