Illustration of Bayesian Inference in Normal Data Models Using Gibbs Sampling

Abstract

The use of the Gibbs sampler as a method for calculating Bayesian marginal posterior and predictive densities is reviewed and illustrated with a range of normal data models, including variance components, unordered and ordered means, hierarchical growth curves, and missing data in a crossover trial. In all cases the approach is straightforward to specify distributionally and to implement computationally, with output readily adapted for required inference summaries.

Key Words:

• Marginalization
• Variance components
• Order-restricted inference
• Hierarchical models
• Missing data
• Nonlinear parameters
• Density estimation