Mixtures of g Priors for Bayesian Variable Selection

By Feng Liang, Rui Paulo, German Molina, Merlise A. Clyde, James O. Berger. 2008

1,218 citations recorded by the source corpus.

Subfields: Management Science and Operations Research, Statistics and Probability

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Citations in the corpus

Bayesian t tests for accepting and rejecting the null hypothesis (2009, methodology): “Liang et al. (2008) provided the corresponding JZS Bayes factors for testing slopes in a regression model.”
Spatial filtering, model uncertainty and the speed of income convergence in Europe (2013, methodology): “Other approaches include mixtures of g-priors and variants of the Zellner-Siow prior (Liang et al. (2008)).”
Local shrinkage rules, Lévy processes and regularized regression (2010, background): “Placing a further prior on τ2 will replicate the mixtures of g-priors that were studied by Liang et al. (2008).”
What Are the Odds? A Practical Guide to Computing and Reporting Bayes Factors (2014, methodology): “edu/ bayesfactor that can be used to estimate Bayes factors based on t values (in the case of t-tests) and R2 values (in the case of regression), as well as sample size (Liang et al., 2008; Rouder & Morey, 2012; Rouder et al., 2009).”
Bayesian Adaptive Sampling for Variable Selection and Model Averaging (2011, methodology): “Mixtures of Zellner’s g-prior, such as the Zellner–Siow Cauchy prior (Zellner and Siow 1980) or the hyper-g prior of Liang et al. (2008) retain the computational simplicity of the original g-prior, but resolve many of the inconsistencies that arise from using a fixed g.”
The Effective Sample Size (2014, methodology): “Other model selection priors which make similar use of n can be found in Bayarri and García-Donato (2007, 2008), Bayarri et al. (2009), George (2000), Liang et al. (2008), Verdinelli and Wasserman (1995), and Zellner (1986).”
Default Bayes factors for ANOVA designs (2012, methodology): “The Zellner–Siow priors lead to consistent Bayes factors if model dimensionality is held constant, but they do not lead to consistent Bayes factors if model dimensionality increases with sample size (Berger, Ghosh, &Mukhopadhyay, 2003; Liang et al., 2008).”
Bayesian Variable Selection Under Collinearity (2015, methodology): “2.1, Equation (5) of Liang et al. 2008).”
MODEL SELECTION FOR HIGH-DIMENSIONAL, MULTI-SEQUENCE CHANGE-POINT PROBLEMS (2012, methodology): “Mixtures of g-priors have been used for high-dimensional Gaussian models in Berger, Ghosh, and Mukhopadhyay (2003) and were shown to have desirable properties in Liang et al. (2008).”
Using Bayes to get the most out of non-significant results (2014, methodology): “…deciding on a default representation of the predictions of the alternative to use in all or most cases (e.g., Jeffreys et al., 1939/1961; Box and Tiao, 1973; Liang et al., 2008; Rouder et al., 2009; Rouder, 2012; Rouder and Morey, 2011; Wetzels and Wagenmakers, 2012; Wetzels et al., 2012).”
Using Stacking to Average Bayesian Predictive Distributions (with Discussion) (2017, methodology): “Accounting for the different complexity, they used the hyper-g prior (Liang et al., 2008).”
Who lies? A large-scale reanalysis linking basic personality traits to unethical decision making (2018, background): “This follows from the fact that the chosen prior distribution ensures consistency, meaning that the Bayes factor for the data-generating model increases as sample size increases (Liang et al., 2008).”
Using MCMC chain outputs to efficiently estimate Bayes factors (2011, methodology): “(13) in Liang et al. (2008), with the prior in their Eq.”
Bayes and empirical-Bayes multiplicity adjustment in the variable-selection problem (2010, background): “Luckily there exists a closed-form approximation to these integrals first noted in Liang et al. (2008). It entails computing the roots of a cubic equation, and extensive numerical experiments show the approximation to be quite accurate.”
Simple relation between Bayesian order-restricted and point-null hypothesis tests (2014, methodology): “Rouder et al. (2009) suggest a Bayes factor for one-sample designs, based on the g prior setting of Liang et al. (2008).”
Rao–Blackwellization for Bayesian Variable Selection and Model Averaging in Linear and Binary Regression: A Novel Data Augmentation Approach (2011, methodology): “BAS uses a one-dimensional Laplace approximation to calculate the marginal likelihood for Zellner-Siow prior (Liang et al. 2008).”