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Activity Number: 303
Type: Contributed
Date/Time: Tuesday, July 31, 2012 : 8:30 AM to 10:20 AM
Sponsor: Section on Statistics and the Environment
Abstract - #306144
Title: Modeling Low-Rank Spatially Varying Cross-Covariances Using Predictive Processes with Application to Soil Nutrient Data
Author(s): Rajarshi Guhaniyogi*+ and Rajarshi Guhaniyogi and Andrew O. Finley and Sudipto Banerjee and Rich Kobe
Companies: and and Michigan State University and University of Minnesota and Michigan State University
Address: 516 University Avenue SE, Minneapolis, MN, 55414, United States
Keywords: spatial ; low rank model ; multivariate model ; cross covariance ; large datasets ; matrix algorithm

We extend earlier work on hierarchical multivariate spatial models to accommodate non-stationarity in the correlations among the outcomes as well as capturing the underlying spatial associations. Direct application of such multivariate models to even moderatesized spatial datasets is often computationally infeasible because of the large number of parameters used to describe the nonstationary multivariate structures and cubic order matrix algorithms involved in estimation. Here, we discuss approaches that help overcome these hurdles without sacri?cing richness in modeling. Our methodological contribution comprises a new class of low-rank spatially-varying cross-covariance matrices that are non-degenerate and that e?ectively capture nonstationary covariances among the multiple outcomes. We provide theoretical and modeling insight into these constructions and elucidate certain implications of some common structural assumptions in building cross-covariance matrices. From a data analytic standpoint, we apply our methods to a soil nutrients dataset collected at La Selva Biological Station, Costa Rica.

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