Fast Bayesian model assessment for nonparametric additive regression

S. McKay Curtis, Sayantan Banerjee and Subhashis Ghosal

Computational Statistics & Data Analysis, 2014, vol. 71, issue C, 347-358

Abstract: Variable selection techniques for the classical linear regression model have been widely investigated. Variable selection in fully nonparametric and additive regression models has been studied more recently. A Bayesian approach for nonparametric additive regression models is considered, where the functions in the additive model are expanded in a B-spline basis and a multivariate Laplace prior is put on the coefficients. Posterior probabilities of models defined by selection of predictors in the working model are computed, using a Laplace approximation method. The prior times the likelihood is expanded around the posterior mode, which can be identified with the group LASSO, for which a fast computing algorithm exists. Thus Markov chain Monte-Carlo or any other time consuming sampling based methods are completely avoided, leading to quick assessment of various posterior model probabilities. This technique is applied to the high-dimensional situation where the number of parameters exceeds the number of observations.

Keywords: Group LASSO; Laplace approximation; Model uncertainty; Penalized regression; Variable selection (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:71:y:2014:i:c:p:347-358

DOI: 10.1016/j.csda.2013.05.012

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