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This paper presents a unified treatment of Gaussian process models thatextends to data from the exponential dispersion family and to survival data.Our specific interest is in the analysis of data sets with predictors that havean a priori unknown form of possibly nonlinear associations to the response.The modeling approach we describe incorporates Gaussian processes in ageneralized linear model framework to obtain a class of nonparametricregression models where the covariance matrix depends on the predictors. Weconsider, in particular, continuous, categorical and count responses. We alsolook into models that account for survival outcomes. We explore alternativecovariance formulations for the Gaussian process prior and demonstrate theflexibility of the construction. Next, we focus on the important problem ofselecting variables from the set of possible predictors and describe a generalframework that employs mixture priors. We compare alternative MCMC strategiesfor posterior inference and achieve a computationally efficient and practicalapproach. We demonstrate performances on simulated and benchmark data sets.

Variable Selection for Nonparametric Gaussian Process Priors: Models and Computational Strategies