Local Likelihood Estimation for Covariance Functions with Spatially Varying Parameters

• Activity Number: 91
• Type: Invited
• Date/Time: Sunday, August 9, 2015 : 9:30 PM to 10:15 PM
• 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: Spatial statistics ; Gaussian processes ; Nonstationary spatial modeling ; Computational methods

Abstract

In spite of the interest in and appeal of convolution approaches for nonstationary spatial modeling, off-the-shelf software for model fitting does not as of yet exist. Current convolution-based models are highly flexible but also highly difficult to fit, even with relatively small data sets, making it difficult to compare new methodology in nonstationary modeling with other existing nonstationary methods. Here, we present a simplified version of the nonstationary spatial model introduced by Paciorek and Schervish (2006) in which the locally varying geometric anisotropies are a discrete mixture of basis kernels, similar to the kernel convolution approach in Higdon (1998), while also allowing the underlying correlation structure to be specified by the modeler. The model can be extended to allow other properties to vary over space as well, such as the variance and nugget effect. Estimation of the spatially varying features will be done locally, similar to the work in Fuentes (2002), and then smoothed over space. This presentation will demonstrate an efficient R package that can quickly perform a full spatial analysis of a nonstationary data set.