Graphs and stochastic relaxation for hierarchical Bayes modelling.

This expository paper describes two useful tools for the statistical analysis of processes that generate repeated measures and longitudinal data. The first tool is a graph for a visual description of dependency structures. The second tool is a stochastic relaxation method ('Gibbs sampling') for fitting hierarchical Bayes models. Graphs are concise and accessible summaries of stochastic models. Graphs aid communications between statistical and subject-matter scientists, during which formulations of scientific questions are modified. An uncluttered picture of the dependency structure of a model augments effectively its corresponding formulaic description. Stochastic relaxation is a computationally intense method that allows experimentation with broader classes of models than were previously thought feasible because of analytic intractability. Stochastic relaxation is intuitive and easily described to non-statisticians. Several sample graphs show how hierarchical Bayes models can use stochastic relaxation to obtain their fits. An example based on estimating drug shelf-life demonstrates some uses of graphs and stochastic relaxation compared with several frequentist growth curve analyses that use restricted maximum likelihood and generalized estimating equations approaches.