Fully Bayes factors with a generalized g-prior

By Yuzo Maruyama, Edward I. George. 2008

118 citations recorded by the source corpus.

For the normal linear model variable selection problem, we propose selection criteria based on a fully Bayes formulation with a generalization of Zellner's $g$-prior which allows for $p>n$. A special case of the prior formulation is seen to yield tractable closed forms for marginal densities and Bayes factors which reveal new model evaluation characteristics of potential interest.

Subfields: Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/0d9705049cb7af7a7d13103c678fce15ab81d814

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In Control and Systems Engineering

In Statistics and Probability

Citations in the corpus

Mixtures of g-priors for Bayesian model averaging with economic applications (2010, unknown): “The resulting hierarchical prior over model space is less restrictive than the one with fixed θ and the choice of m is shown in Ley and Steel (2009) not to matter too much in practice.”
Mixtures of g-Priors in Generalized Linear Models (2015, methodology): “…literature, including Copas (1983, 1997); Kass and Wasserman (1995); Hansen and Yu (2003); Rathbun and Fei (2006); Marin and Robert (2007); Wang and George (2007); Fouskakis, Ntzoufras, and Draper (2009); Gupta and Ibrahim (2009); Sabanés Bové and Held (2011); Hanson, Branscum, and Johnson (2014);…”
Decoupling Shrinkage and Selection in Bayesian Linear Models: A Posterior Summary Perspective (2014, background): “…these hyperparameters recommended in the literature include: {a = 1, b = 1, d = 0, ρφ = 1/(1 + n)} (Cui and George 2008), {a = 1/2, b = 1 (b = n), c = 0, d = 0, ρφ = 1/(1 + n)} (Liang et al. 2008), and {a = 1, b = 1, c = −3/4, d = (n− 5)/2 − pφ/2 + 3/4, ρφ = 1/(1 + n)} (Maruyama and George 2011).”
Model Averaging and Its Use in Economics (2017, methodology): “Generalized Linear Models (GLMs) describe a more general class of models (McCullagh and Nelder, 1989) that covers the normal linear regression model but also regression models where the response variable is non-normal, such as binomial (e.g. logistic or logit regression models, probit models), Poiss”