A Gaussian Process Regression Approach to a Single-Index Model

• Activity Number: 676
• Type: Contributed
• Date/Time: Thursday, August 5, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Taeryon Choi*+ and Jian Qing Shi and Bo Wang
• Companies: Korea University and University of Newcastle and University of York
• Keywords: Gaussian process prior ; Generalized linear model ; Empirical Bayes Gibbs Sampler ; Marginal likelihood ; MAP

Abstract

We consider a Gaussian process regression approach to analyzing a single-index model from the Bayesian perspective. Specifically, the unknown link function is assumed to be a Gaussian process a priori and a prior on the index vector is considered based on a simple uniform distribution on the unit sphere. The posterior distributions for the unknown parameters are derived, and the posterior inference of the proposed approach is performed via Markov chain Monte Carlo methods based on them. Particularly, in estimating the hyperparameters, different numerical schemes are implemented : fully Bayesian method and empirical Bayes method. Numerical illustration of the proposed approach is also made using simulation data as well as well-known real data. In addition, we discuss the theoretical aspect of the proposed method in terms of posterior consistency.