Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Data

• Activity Number: 100
• Type: Invited
• Date/Time: Monday, August 4, 2014 : 8:30 AM to 10:20 AM
• Sponsor: International Indian Statistical Association
• Author(s): Sudipto Banerjee*+ and Abhirup Datta and Andrew Oliver Finley and Alan Gelfand
• Companies: University of Minnesota and University of Minnesota and Michigan State University and Duke University
• Keywords: Bayesian modeling ; High-dimensional Kriging ; Nearest Neighbor Gaussian Process ; Spatial Processes

Abstract

Use of spatial process models to analyze and infer about spatially referenced datasets has become increasingly popular over the last decade. However, estimating such models entail computationally intensive algorithms involving high-dimensional matrices, often without exploitable structure. When the number of locations become large, such methods cease to be feasible. We exploit a familiar geostatistical notion of spatial correlation being strongest among nearest neighbors to construct a well-defined class of Nearest Neighbor Gaussian Process (NNGP) models for spatial data. This process dramatically reduces computational complexity for our model without compromising on inferential performance. A Bayesian hierarchical framework is proposed, where the number of floating point operations is linear in the number of locations, thereby imparting scalable to large data. We use simulation experiments to illustrate the huge computational benefits and excellence in inferential performance over competing approaches such as low rank models. Finally, we present analysis of a massive forest biomass inventory dataset using a spatially varying NNGP model to infer about forest biomass processes.