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February 2011 Variable Selection for Nonparametric Gaussian Process Priors: Models and Computational Strategies
Terrance Savitsky, Marina Vannucci, Naijun Sha
Statist. Sci. 26(1): 130-149 (February 2011). DOI: 10.1214/11-STS354

Abstract

This paper presents a unified treatment of Gaussian process models that extends to data from the exponential dispersion family and to survival data. Our specific interest is in the analysis of data sets with predictors that have an a priori unknown form of possibly nonlinear associations to the response. The modeling approach we describe incorporates Gaussian processes in a generalized linear model framework to obtain a class of nonparametric regression models where the covariance matrix depends on the predictors. We consider, in particular, continuous, categorical and count responses. We also look into models that account for survival outcomes. We explore alternative covariance formulations for the Gaussian process prior and demonstrate the flexibility of the construction. Next, we focus on the important problem of selecting variables from the set of possible predictors and describe a general framework that employs mixture priors. We compare alternative MCMC strategies for posterior inference and achieve a computationally efficient and practical approach. We demonstrate performances on simulated and benchmark data sets.

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Terrance Savitsky. Marina Vannucci. Naijun Sha. "Variable Selection for Nonparametric Gaussian Process Priors: Models and Computational Strategies." Statist. Sci. 26 (1) 130 - 149, February 2011. https://doi.org/10.1214/11-STS354

Information

Published: February 2011
First available in Project Euclid: 9 June 2011

zbMATH: 1222.65017
MathSciNet: MR2849913
Digital Object Identifier: 10.1214/11-STS354

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.26 • No. 1 • February 2011
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