Empirical Bayes vs. Fully Bayes Variable Selection

By Wen Cui, Edward I. George. 2008

147 citations recorded by the source corpus.

Abstract For the problem of variable selection for the normal linear model, fixed penalty selection criteria such as AIC, C p , BIC and RIC correspond to the posterior modes of a hierarchical Bayes model for various fixed hyperparameter settings. Adaptive selection criteria obtained by empirical Bayes estimation of the hyperparameters have been shown by George and Foster [2000. Calibration and Empirical Bayes variable selection. Biometrika 87(4), 731–747] to improve on these fixed selection criteria. In this paper, we study the potential of alternative fully Bayes methods, which instead margin out the hyperparameters with respect to prior distributions. Several structured prior formulations are considered for which fully Bayes selection and estimation methods are obtained. Analytical and simulation comparisons with empirical Bayes counterparts are studied.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7a0a1101d3a8ce5a128f6961fa57e234c628c0b8

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In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

Model Averaging and Its Use in Economics (2017, background): “veraged over all models. Liang et al. (2008) propose speciﬁc ways of estimating gin this context. There is some evidence in the literature regarding comparisons between fully Bayes and EB procedures: Cui and George (2008) largely favour (global) EB in the context of known ˙and k = n, whereas Liang e”
Fully Bayes factors with a generalized g-prior (2008, methodology): “Both Cui and George (2008) and Liang et al. (2008) proposed using g-priors with priors of the form p(g) = (a+1)−1(1 + g)−a−2,(2.14) the subclass of (2.13) with b= 0.”
On the Frequentist Properties of Bayesian Nonparametric Methods (2016, methodology): “Cui and George, 2008.”
Bayes and empirical-Bayes multiplicity adjustment in the variable-selection problem (2010, background): “Fully Bayesian variable-selection priors have been discussed by Ley and Steel (2009), Cui and George (2008) and Carvalho and Scott (2009), among others.”
A Default Bayesian Hypothesis Test for ANOVA Designs (2012, methodology): “3.3 Hyper-g Priors As an alternative to the JZS prior, Liang et al. (2008) proposed a family of prior distributions on g and termed this the hyper-g approach: p(g) = a − 2 2 (1 + g)−a/2 g > 0, which is a proper distribution if a > 2 (Strawderman 1971; Cui and George 2008).”
Mixtures of g-priors for Bayesian model averaging with economic applications (2010, unknown): “Cui and George (2008) propose to use a = 4 in the context of model selection with known σ. Bottolo and Richardson (2008) adopt a hyper-g prior with a = 2, but make it proper by truncating the right tail at max{n, k2}, which is the benchmark value for g proposed by Fernández et al. (2001a).”
Mixtures of g-Priors in Generalized Linear Models (2015, methodology): “…on the hyper parameter g in (4), include the Cauchy prior of Zellner and Siow (1980), the hyper-g and related hyper-g/n priors (Liang et al. 2008; Cui and George 2008), the Beta-prime prior (Maruyama and George 2011), the robust prior (Bayarri et al. 2012), and the intrinsic prior (Casella and…”
Criteria for Bayesian model choice with application to variable selection (2012, background): “…Kass and Wasserman (1995), Berger and Pericchi (1996), Moreno, Bertolino and Racugno (1998), De Santis and Spezzaferri (1999), Pérez and Berger (2002), Bayarri and Garćıa-Donato (2008), Liang et al. (2008), Cui and George (2008), Maruyama and George (2008), Maruyama and Strawderman (2010).”
Benchmark Priors Revisited: On Adaptive Shrinkage and the Supermodel Effect in Bayesian Model Averaging (2009, unknown): “Only few papers have applied such hyperpriors in BMA so far: Among them are Strachan and van Dijk (2004), Cui and George (2008), Liang et al.”
The Median Probability Model and Correlated Variables (2018, background): “Beta-binomial Prior: It is generally acknowledged (Cui and George 2008; Ley and Steel 2009; Scott and Berger 2010) that assigning equal prior probability to all models is a poor choice, since it does not adjust for the multiple testing that is effectively being done in variable selection.”
Mixtures of g Priors for Bayesian Variable Selection (2008, methodology): “Interestingly, we found that all of the fully Bayes mixture g priors do as well as the global EB with model selection, except under the null model, whereas Cui and George (2007) found that the global EB outperformed fully Bayes procedures (under the assumption of known φ). We have used a uniform pri”