Hyper-g Priors for Generalized Linear Models

Details Hyper-g Priors for Generalized Linear Models Hyper-g Priors for Generalized Linear Models

2010-08-09

arxiv.org/abs/1008.1550v1

Published in Bayesian Analysis (2011) volume 6, number 3, pages 387-410

Statistics

Methodology

30 pages, 12 figures, poster contribution at ISBA 2010

Scientific paper

10.1214/11-BA615

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.

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