title: Graphs and stochastic relaxation for hierarchical Bayes modelling.
abstract: 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.
authors: Department of Community Health, Brown University, Providence, RI 02912.
authors: N
authors: N
authors: Lange
mesh_terms: D001499:Bayes Theorem; D008137:Longitudinal Studies; D015233:Models, Statistical; D009010:Monte Carlo Method; D013269:Stochastic Processes