 
Summary: A MCMC Algorithm to Fit a General
Exchangeable Model
Jim Albert \Lambda
Bowling Green State University
and Duke University
September, 1994
Abstract
Consider the exchangeable Bayesian hierarchical model where observations y i
are in
dependently distributed from sampling densities with unknown means, the means ¯ i
are
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
