Nonparametric Regression using Nonstationary Gaussian Processes

• Activity Number: 205
• Type: Contributed
• Date/Time: Tuesday, August 5, 2003 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Stat. Sciences
• Author(s): Christopher J. Paciorek*+ and Mark J. Schervish
• Companies: Carnegie Mellon University and Carnegie Mellon University
• Keywords: nonparametric ; regression ; nonstationary ; covariance ; Gaussian process

Abstract

Bayesian methods for nonparametric regression have become popular recently. One approach uses a Gaussian process prior for the unknown function, which provides a method for flexible curve and surface-fitting. One challenge is to model functions that are spatially inhomogeneous, i.e., functions that are not equally smooth throughout the covariate space. For these situations, Bayesian free-knot spline methods with varying number and locations of knots have been used. An alternative is to use Gaussian process models with a nonstationary covariance function. I generalize the nonstationary covariance that Higdon, Swall, and Kern (1999) used for spatial data to give a class of nonstationary covariance functions based on familiar stationary covariances, including a nonstationary Matern covariance. Using this Matern nonstationary covariance, I parameterize a Bayesian nonparametric regression model. The model is fit via MCMC, with particular proposals that facilitate hyperparameter mixing. I show the model is competitive with other adaptive methods for a set of real and simulated problems. I also comment on using these nonstationary covariance functions to model spatial data.