Griffin, Jim E.; Brown, Philip J. Inference with normal-gamma prior distributions in regression problems. (English) Zbl 1330.62128 Bayesian Anal. 5, No. 1, 171-188 (2010). Summary: 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 [T. Park and G. Casella, J. Am. Stat. Assoc. 103, No. 482, 681–686 (2008; Zbl 1330.62292)], 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. Cited in 2 ReviewsCited in 85 Documents MSC: 62F15 Bayesian inference 62J07 Ridge regression; shrinkage estimators (Lasso) 60J22 Computational methods in Markov chains 65C60 Computational problems in statistics (MSC2010) 65C05 Monte Carlo methods Keywords:multiple regression; \(p>n\); normal-gamma prior; “spike-and-slab” prior; Bayesian Lasso; posterior moments; shrinkage; scale mixture of normals; Markov chain Monte Carlo Citations:Zbl 1330.62292 PDF BibTeX XML Cite \textit{J. E. Griffin} and \textit{P. J. Brown}, Bayesian Anal. 5, No. 1, 171--188 (2010; Zbl 1330.62128) Full Text: DOI Euclid OpenURL