Flexible Link Functions in Nonparametric Binary Regression with Gaussian Process Priors

• Activity Number: 598
• Type: Topic Contributed
• Date/Time: Wednesday, August 3, 2016 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Xia Wang* and Dan Li and Lizhen Lin and Dipak Dey
• Companies: University of Cincinnati and University of Cincinnati and The University of Texas and University of Connecticut
• Keywords: Gaussian Process ; Generalized Extreme Value Distribution ; Markov chain Monte Carlo ; Posterior Consistency

Abstract

Gaussian processes have been widely used to model nonlinear systems; in particular to model the latent structure in a binary regression model allowing nonlinear functional relationship between covariates and the expectation of binary outcomes. A critical issue in modeling binary response data is the appropriate choice of link functions. Commonly adopted link functions such as probit or logit links have fixed skewness and lack the flexibility to allow the data to determine the degree of the skewness. To address this limitation, we propose a flexible binary regression model which combines a generalized extreme value link function with a Gaussian process prior on the latent structure. Bayesian computation is employed in model estimation. Posterior consistency of the resulting posterior distribution is demonstrated. The flexibility and gains of the proposed model are illustrated through detailed simulation studies and two real data examples. Empirical results show that the proposed model outperforms a set of alternative models, which only have either a Gaussian process prior on the latent regression function or a Dirichlet prior on the link function.