## Bayesian Analysis

### Hyper-$g$ priors for generalized linear models

#### Abstract

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

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

Dates
First available in Project Euclid: 13 June 2012

https://projecteuclid.org/euclid.ba/1339616469

Digital Object Identifier
doi:10.1214/11-BA615

Mathematical Reviews number (MathSciNet)
MR2843537

Zentralblatt MATH identifier
1330.62058

#### Citation

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. https://projecteuclid.org/euclid.ba/1339616469

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