A COMPARISON OF HIERARCHICAL BAYES AND EMPIRICAL BAYES METHODS WITH A FORESTRY APPLICATION

Gibbs sampling for generating marginal posterior distributions in Bayesian analysis is introduced to the forestry literature. Hierarchical Bayes and (parametric) empirical Bayes methods are compared theoretically and with a practical example. It is shown that in the latter procedures, the error due to estimating the hyperparameters from the marginal distribution of the data is ignored. This results in underestimating the scale of the marginal posterior distributions.