Abstract

Specification of the linear predictor for a generalised linear model requires determining which variables to include. We consider Bayesian strategies for performing this variable selection. In particular we focus on approaches based on the Gibbs sampler. Such approaches may be implemented using the publically available software BUGS. We illustrate the methods using a simple example. BUGS code is provided in an appendix. 1 Introduction In a Bayesian analysis of a generalised linear model, model uncertainty may be incorporated coherently by specifying prior probabilities for plausible models and calculating posterior probabilities using f(mjy) = f(m)f(yjm) P m2M f(m)f(y jm) ; m 2 M (1.1) where m denotes the model, M is the set of all models under consideration, f (m) is the prior probability of model m and f (yjm; fi m ) the likelihood of the data y under model m. The observed data y contribute to the posterior model probabilities through f(yjm), the marginal likelihood calculated...

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