Bayesian Analysis

Hyper-$g$ priors for generalized linear models

Daniel Sabanés Bové and Leonhard Held

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We develop an extension of the classical Zellner's $g$-prior to generalized linear models. 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.

Article information

Bayesian Anal., Volume 6, Number 3 (2011), 387-410.

First available in Project Euclid: 13 June 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62C12: Empirical decision procedures; empirical Bayes procedures
Secondary: 62F15: Bayesian inference 62J12: Generalized linear models 62P10: Applications to biology and medical sciences

$g$-prior generalized linear model integrated Laplace approximation variable selection fractional polynomials


Sabanés Bové, Daniel; Held, Leonhard. Hyper-$g$ priors for generalized linear models. Bayesian Anal. 6 (2011), no. 3, 387--410. doi:10.1214/11-BA615.

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