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March 2010 Inference with normal-gamma prior distributions in regression problems
Philip J. Brown, Jim E. Griffin
Bayesian Anal. 5(1): 171-188 (March 2010). DOI: 10.1214/10-BA507


This paper considers the effects of placing an absolutely continuous prior distribution on the regression coefficients of a linear model. We show that the posterior expectation is a matrix-shrunken version of the least squares estimate where the shrinkage matrix depends on the derivatives of the prior predictive density of the least squares estimate. The special case of the normal-gamma prior, which generalizes the Bayesian Lasso (Park and Casella 2008), is studied in depth. We discuss the prior interpretation and the posterior effects of hyperparameter choice and suggest a data-dependent default prior. Simulations and a chemometric example are used to compare the performance of the normal-gamma and the Bayesian Lasso in terms of out-of-sample predictive performance.


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Philip J. Brown. Jim E. Griffin. "Inference with normal-gamma prior distributions in regression problems." Bayesian Anal. 5 (1) 171 - 188, March 2010.


Published: March 2010
First available in Project Euclid: 22 June 2012

zbMATH: 1330.62128
MathSciNet: MR2596440
Digital Object Identifier: 10.1214/10-BA507

Keywords: "Spike-and-slab" prior , $p>n$ , Bayesian lasso , Markov chain Monte Carlo , multiple regression , normal-gamma prior , Posterior moments , Scale mixture of normals , shrinkage

Rights: Copyright © 2010 International Society for Bayesian Analysis


Vol.5 • No. 1 • March 2010
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