A MCMC algorithm to fit a general exchangeable model

Abstract

Consider the exchangeable Bayesian hierarchical model where observations y_i are independently distributed from sampling densities with unknown means, the means µi, 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 distribution 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 algorithm. Methods of model checking and extensions to hierarchical regression modeling are discussed.

Keywords:

• hierarchical model
• Gibbs sampler
• Metropolis algorithm
• logistic model
• output analysis