Regression-Based Covariance Functions for Nonstationary Spatial Modeling

• Activity Number: 302
• Type: Topic Contributed
• Date/Time: Tuesday, August 11, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics and the Environment
• Author(s): Mark Risser* and Catherine Calder
• Companies: The Ohio State University and The Ohio State University
• Keywords: Bayesian modeling ; Covariance regression ; Gaussian Processes ; Precipitation ; Spatial Statistics

Abstract

A key component of models for continuously-indexed spatial data is the covariance function, which is traditionally assumed to belong to a parametric class of stationary models. Stationarity is rarely a realistic assumption; however, more appropriate nonstationary methods often involve high-dimensional parameter spaces which leads to difficulties in model fitting and interpretability. To overcome this issue, we build on the growing literature of covariate-driven nonstationary spatial modeling. Using process convolution techniques, we propose a Bayesian model for continuously-indexed spatial data based on a flexible parametric covariance regression structure for a convolution-kernel covariance matrix. The resulting model is a parsimonious representation of the kernel process, and we provide a description of the resulting nonstationary covariance function and the interpretational benefits in the kernel parameters. Furthermore, we show that our model provides a practical compromise between stationary and highly parameterized nonstationary spatial covariance functions that do not perform well in practice. We illustrate our approach through an analysis of annual precipitation data.