ABSTRACT
ABSTRACT In this chapter, we describe two useful tools for the Bayesian analysis of generalized linear models (GLM's) and their extensions. The first is a graphical modelling approach for representing the conditional independence assumptions and qualitative structure underlying a statistical model. The second is the WinBUGS statistical software, which implements a Markov chain Monte Carlo approach to Bayesian inference. Graphical models form the central construct of both the statistical model and the software by providing a direct link between the model description and the computational solutions to the associated inference problem. We describe how these parallels are exploited by the WinBUGS software and show how this leads to a readily extensible programming environment for complex Bayesian modeling. The remainder of the chapter offers practical guidelines for implementing Bayesian GLM's using the WinBUGS software. Particular emphasis is placed on the flexibility of both the Bayesian graphical modeling approach and the WinBUGS program to extend the standard GLM framework by accommodating additional sources of complexity such as correlated data structures, overdispersion, measurement error, missing data, outlying observations and so on.
