Open Access
VOL. 8 | 2012 Bayesian prediction with adaptive ridge estimators
David G.T. Denison, Edward I. George

Editor(s) Dominique Fourdrinier, Éric Marchand, Andrew L. Rukhin

Inst. Math. Stat. (IMS) Collect., 2012: 215-234 (2012) DOI: 10.1214/11-IMSCOLL815


The Bayesian linear model framework has become an increasingly popular building block in regression problems. It has been shown to produce models with good predictive power and can be used with basis functions that are nonlinear in the data to provide flexible estimated regression functions. Further, model uncertainty can be accounted for by Bayesian model averaging. We propose a simpler way to account for model uncertainty that is based on generalized ridge regression estimators. This is shown to predict well and to be much more computationally efficient than standard model averaging methods. Further, we demonstrate how to efficiently mix over different sets of basis functions, letting the data determine which are most appropriate for the problem at hand.


Published: 1 January 2012
First available in Project Euclid: 14 March 2012

zbMATH: 1326.62059
MathSciNet: MR3202513

Digital Object Identifier: 10.1214/11-IMSCOLL815

Primary: 62F15 , 62J05

Keywords: Bayesian model averaging , Generalized ridge regression , prediction , regression splines , shrinkage

Rights: Copyright © 2012, Institute of Mathematical Statistics

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