Criteria for Bayesian model choice with application to variable selection

By Maria J. Bayarri, James O. Berger, A. Forte, G. Garc'ia-Donato. 2012

317 citations recorded by the source corpus.

In objective Bayesian model selection, no single criterion has emerged as dominant in defining objective prior distributions. Indeed, many criteria have been separately proposed and utilized to propose differing prior choices. We first formalize the most general and compelling of the various criteria that have been suggested, together with a new criterion. We then illustrate the potential of these criteria in determining objective model selection priors by considering their application to the problem of variable selection in normal linear models. This results in a new model selection objective prior with a number of compelling properties.

Subfields: Artificial Intelligence, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/8f1593a7a2acc24533e51e8d52bcadb8c5509d11

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Citations in the corpus

On p-Values and Bayes Factors (2018, background): “In the absence of substantive prior information, it is common to assign the g-prior (Zellner 1986) θ |σ2, H1 ∼ N(0, g σ2 (XTX)−1) (22) for fixed g > 0 to θ, which is invariant with respect to location-scale transformations of the covariates (Bayarri et al. 2012).”
The Median Probability Model and Correlated Variables (2018, methodology): “First, using predictive matching arguments (Berger and Pericchi 2001; Bayarri et al. 2012; Fouskakis et al. 2018), we provide new arguments for the suitability of g-type priors as opposed to independent product priors.”
Generalized Fiducial Inference: A Review and New Results (2016, background): “Examples of recent breakthroughs related to reference prior and model selection are Bayarri et al. (2012), Berger (1992), Berger and Sun (2008), Berger, Bernardo, and Sun (2009), and Berger, Bernardo, and Sun (2012).”
Mixtures of g-Priors in Generalized Linear Models (2015, methodology): “5, br = 1, and ρr = 1/(1 + pM) are recommended (Bayarri et al. 2012), under which the prior (34) reduces to a truncated Gamma, with a conjugate updating:”
J. B. S. Haldane's Contribution to the Bayes Factor Hypothesis Test (2015, methodology): “In addition, Bayes factors can be used for model-averaging (Hoeting et al., 1999) and variable selection (Bayarri et al., 2012).”
A Tutorial on Fisher Information (2017, methodology): “…the Jeffreys’s prior, a2 noninformative prior commonly used for estimation problems and for nuisance parameters in a3 Bayesian hypothesis test (e.g., Bayarri et al., 2012; Dawid, 2011; Jeffreys, 1961; Liang et al., 2008;4 Li and Clyde, 2015; Ly et al., 2015; Ly et al., 2016d; Ly et al., 2016c; Ly…”
Joint estimation of multiple networks from time course data (2013, methodology): “We chose to employ the g-prior due to Zellner (1986), where following George and Foster (2000) we used (conditional) empirical Bayes to select the g hyperparameter.”
Mixtures of g-priors for Bayesian model averaging with economic applications (2010, methodology): “prior on common parameters, but the prior structure used here can be motivated through invariance arguments (see Berger, Pericchi and Varshavsky, 1998) and is generally accepted to be a reasonable choice. One advantage of this prior is that we only need to choose a single scalar parameter g. A large”
Safe Testing (2019, methodology): “Let fvs(p) := −ep log p, a quantity sometimes called the Vovk-Sellke bound (Bayarri et al., 2016)), having roots in earlier work by by Vovk (1993) and Sellke et al.”
Model Averaging and Its Use in Economics (2017, methodology): “For the regression coefficients βj , they propose a g-prior specification (Zellner, 18See Bayarri et al. (2012) for the precise definition of these criteria for “objective” model selection priors.”
Safe models for risky decisions (2017, background): “Originally, Bechara et al. (1994) developed the IGT to distinguish decision-making strategies of patients with lesions to the ventromedial prefrontal cortex from the ones of healthy controls (see also Bechara et al.”
Beyond subjective and objective in statistics (2015, background): “It is difficult to see, and no information about this was provided by Jaynes himself, how it can be possible to translate the unspecific information of knowing of some outliers in many kinds of situations, some of which are more or less related, but none identical (say) to the problem at hand, into ”