Low-Rank Spatially Varying Cross-Covariance Estimation

• Activity Number: 396
• Type: Invited
• Date/Time: Tuesday, August 11, 2015 : 2:00 PM to 3:50 PM
• Sponsor: JABES-Journal of Agricultural, Biological, and Environmental Statistics
• Author(s): Rajarshi Guhaniyogi* and Andrew O. Finley and Sudipto Banerjee and Rich Kobe
• Companies: UC Santa Cruz and Michigan State University and UCLA and Michigan State University
• Keywords: large spatial data ; nonstationary cross covariance ; predictive process model ; soil nutrient dataset

Abstract

Advances in geospatial technologies have created data-rich environments which provide extraordinary opportunities to understand the complexity of large and spatially indexed data in natural science. Our current application concerns analysis of soil nutrients data collected at La Selva Biological Station, Costa Rica, where inferential interest lies in capturing the spatially varying relationships among the nutrients. The objective here is to interpolate not just the nutrients across space, but also associations among the nutrients that are posited to vary spatially. This requires spatially varying cross-covariance models. Here we develop fully process-based low-rank but non-degenerate spatially varying cross-covariance processes that can effectively interpolate cross-covariances at arbitrary locations. We show how a particular low-rank process, the predictive process, can be effectively deployed to model non-degenerate cross-covariance processes. We produce substantive inferential tools such as maps of nonstationary cross-covariances that constitute the premise of further mechanistic modeling and have hitherto not been easily available for environmental scientists and ecologists.