Spatial Smoothing Using a New Class of Nonstationary Covariance Functions

• Activity Number: 147
• Type: Topic Contributed
• Date/Time: Monday, August 9, 2004 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Christopher J. Paciorek*+
• Companies: Harvard School of Public Health
• Keywords: nonstationary covariance ; Gaussian process ; spatial smoothing ; matern covariance ; nonstationary kriging

Abstract

We introduce a class of nonstationary covariance functions for spatial modeling. Nonstationary covariance functions allow Gaussian process (GP) models to adapt to spatial surfaces whose smoothness varies with location. The class includes a nonstationary version of the matern covariance, which parameterizes the differentiability of the spatial surface. We employ this new nonstationary covariance in a full Bayesian spatial model, parameterizing the nonstationarity in a computationally efficient way that produces nearly stationary local behavior. We also use the new covariance in an ad hoc "nonstationary kriging" method. We perform an extensive assessment of the full Bayesian model and compare it to a stationary GP model, as well as various spatial and general smoothing methods. In simulations, the nonstationary GP model adapts to variable smoothness while standard spatial methods do not. On real datasets, the nonstationary GP model outperforms other nonstationary smoothers, as well as the stationary GP model under certain conditions, but also shows evidence of overfitting when the spatial surface is complicated.