Bayesian Analysis

Inference with normal-gamma prior distributions in regression problems

Philip J. Brown and Jim E. Griffin

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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.

Article information

Bayesian Anal., Volume 5, Number 1 (2010), 171-188.

First available in Project Euclid: 22 June 2012

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Zentralblatt MATH identifier

Multiple regression $p>n$ Normal-Gamma prior "Spike-and-slab" prior Bayesian Lasso Posterior moments Shrinkage Scale mixture of normals Markov chain Monte Carlo


Griffin, Jim E.; Brown, Philip J. Inference with normal-gamma prior distributions in regression problems. Bayesian Anal. 5 (2010), no. 1, 171--188. doi:10.1214/10-BA507.

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