Mixtures of g-Priors in Generalized Linear Models

By Yingbo Li, Merlise A. Clyde. Journal of the American Statistical Association, 2015

88 citations recorded by the source corpus.

ABSTRACT Mixtures of Zellner’s g-priors have been studied extensively in linear models and have been shown to have numerous desirable properties for Bayesian variable selection and model averaging. Several extensions of g-priors to generalized linear models (GLMs) have been proposed in the literature; however, the choice of prior distribution of g and resulting properties for inference have received considerably less attention. In this article, we unify mixtures of g-priors in GLMs by assigning the truncated Compound Confluent Hypergeometric (tCCH) distribution to 1/(1 + g), which encompasses as special cases several mixtures of g-priors in the literature, such as the hyper-g, Beta-prime, truncated Gamma, incomplete inverse-Gamma, benchmark, robust, hyper-g/n, and intrinsic priors. Through an integrated Laplace approximation, the posterior distribution of 1/(1 + g) is in turn a tCCH distribution, and approximate marginal likelihoods are thus available analytically, leading to “Compound Hypergeometric Information Criteria” for model selection. We discuss the local geometric properties of the g-prior in GLMs and show how the desiderata for model selection proposed by Bayarri et al., such as asymptotic model selection consistency, intrinsic consistency, and measurement invariance may be used to justify the prior and specific choices of the hyper parameters. We illustrate inference using these priors and contrast them to other approaches via simulation and real data examples. The methodology is implemented in the R package BAS and freely available on CRAN. Supplementary materials for this article are available online.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/bf44684616ad3de2453153b7693bfa8360042f51

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Citations in the corpus

On the Use of Cauchy Prior Distributions for Bayesian Logistic Regression (2015, background): “…distributions for regression coefficients frequently arise in Bayesian variable selection, for regression models with binary or categorical response variables (Holmes and Held, 2006; Mitra and Dunson, 2010; Ghosh and Clyde, 2011; Ghosh et al., 2011; Ghosh and Reiter, 2013; Li and Clyde, 2015).”
Model Averaging and Its Use in Economics (2017, methodology): “The priors on the model parameters designed for GLMs in Li and Clyde (2017) employ a different type of “centering” (induced by the observed information matrix at the MLE of the coefficients), leading to a g-prior that displays local orthogonality properties at the MLE.”
A Tutorial on Fisher Information (2017, methodology): “This section outlines how Fisher information can be used to define the Jeffreys’s prior, a default prior commonly used for estimation problems and for nuisance parameters in a Bayesian hypothesis test (e.g., Bayarri et al., 2012; Dawid, 2011; Gronau, Ly and Wagenmakers, 2017; Jeffreys, 1961; Liang e”