Testing restrictions in hierarchical normal data models using Gibbs sampling*1

Abstract

The problem of testing a set of restrictions in a complex hierarchical normal model is considered and a numerical Bayesian method proposed. The suggested approach is based on the comparison of two density functions easily obtained as a by-product of the Gibbs sampling. The procedure is easy to implement and can be computed also when some priors in the hierarchy are diffuse. Monte Carlo simulations show that the procedure has good statistical properties.