Hyper-g Priors for Generalized Linear Models

TL;DR

This paper introduces a flexible extension of Zellner's g-prior for generalized linear models, enabling efficient Bayesian inference and variable selection through novel hyperprior handling, Laplace approximation, and a tuning-free sampler.

Contribution

It extends g-priors to generalized linear models with flexible hyperprior choices, and develops fast inference methods including Laplace approximation and a tuning-free MCMC sampler.

Findings

Effective variable selection demonstrated on diabetes data

Flexible hyper-g prior framework enhances model adaptability

Fast inference methods improve computational feasibility

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.