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December 2022 Power-Expected-Posterior Priors as Mixtures of g-Priors in Normal Linear Models
Dimitris Fouskakis, Ioannis Ntzoufras
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Bayesian Anal. 17(4): 1073-1099 (December 2022). DOI: 10.1214/21-BA1288


One of the main approaches used to construct prior distributions for objective Bayes methods is the concept of random imaginary observations. Under this setup, the expected-posterior prior (EPP) offers several advantages, among which it has a nice and simple interpretation and provides an effective way to establish compatibility of priors among models. In this paper, we study the power-expected-posterior prior as a generalization to the EPP in objective Bayesian model selection under normal linear models. We prove that it can be represented as a mixture of g-prior, like a wide range of prior distributions under normal linear models, and thus posterior distributions and Bayes factors are derived in closed form, keeping therefore its computational tractability. Following this result, we can naturally prove that desiderata (criteria for objective Bayesian model comparison) hold for the PEP prior. Comparisons with other mixtures of g-prior are made and results are presented in simulated and real-life datasets.


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Dimitris Fouskakis. Ioannis Ntzoufras. "Power-Expected-Posterior Priors as Mixtures of g-Priors in Normal Linear Models." Bayesian Anal. 17 (4) 1073 - 1099, December 2022.


Published: December 2022
First available in Project Euclid: 27 September 2021

Digital Object Identifier: 10.1214/21-BA1288

Keywords: Bayesian model comparison , expected-posterior priors , imaginary training samples , mixtures of g-priors , objective priors


Vol.17 • No. 4 • December 2022
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