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Inference with normal-gamma prior distributions in regression problems

Griffin, Jim E., Brown, Philip J. (2010) Inference with normal-gamma prior distributions in regression problems. Bayesian Analysis, 5 (1). pp. 171-188. ISSN 1936-0975. (doi:10.1214/10-BA508) (KAR id:23866)

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Official URL:
http://dx.doi.org/10.1214/10-BA507

Abstract

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.

Item Type: Article
DOI/Identification number: 10.1214/10-BA508
Subjects: Q Science > QA Mathematics (inc Computing science) > QA276 Mathematical statistics
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Jim Griffin
Date Deposited: 29 Jun 2011 13:34 UTC
Last Modified: 16 Nov 2021 10:02 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/23866 (The current URI for this page, for reference purposes)
Griffin, Jim E.: https://orcid.org/0000-0002-4828-7368
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