Hyper-g Priors for Generalized Linear Models

Abstract

We develop an extension of the classical Zellner's g-prior to generalized linear models. The prior on the hyperparameter g is handled in a flexible way, so that any continuous proper hyperprior f(g) can be used, giving rise to a large class of hyper-g priors. Connections with the literature are described in detail. A fast and accurate integrated Laplace approximation of the marginal likelihood makes inference in large model spaces feasible. For posterior parameter estimation we propose an efficient and tuning-free Metropolis-Hastings sampler. The methodology is illustrated with variable selection and automatic covariate transformation in the Pima Indians diabetes data set.

30 pages, 12 figures, poster contribution at ISBA 2010

References in corpus (5)

• Optimal predictive model selection
• Bayes and empirical-Bayes multiplicity adjustment in the variable-selection problem
• Fully Bayes factors with a generalized g-prior
• Harold Jeffreys's Theory of Probability Revisited
• Approximating the marginal likelihood using copula

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• Bayesian model selection in additive partial linear models via locally adaptive splines
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• Modeling Sheep pox Disease from the 1994-1998 Epidemic in Evros Prefecture, Greece