Hierarchical Nearest Neighbor Gaussian Process Models for Massive Geo-Statistical Data Sets

• Activity Number: 552
• Type: Topic Contributed
• Date/Time: Wednesday, August 6, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Abhirup Datta*+ and Sudipto Banerjee and Andrew Oliver Finley and Alan Gelfand
• Companies: University of Minnesota and University of Minnesota and Michigan State University and Duke University
• Keywords: Multivariate spatial processes ; Neighbor-based conditioning sets ; Markov Chain Monte Carlo ; Reduced complexity ; Forest biomass data

Abstract

Hierarchical spatial process models are being increasingly deployed for analyzing geo-reference data. However, these models entail onerous computations that become prohibitive as the number of spatial locations become large. As spatial associations are strongest between nearby locations and wane with increasing distances, we propose a class of Nearest Neighbor Gaussian Process (NNGP) models that offer fully Bayesian inference in a coherent stochastic setting. We show that the NNGP processes conform to Kolmogorov's consistency criteria providing legitimate finite-dimensional Gaussian densities with sparse precision matrices and can be seamlessly embedded within a rich and flexible hierarchical modeling framework. We develop a computationally efficient Markov chain Monte Carlo algorithm where floating point operations (flops) per iteration is linear in the number of spatial locations ensuring massive scalability. We use simulated datasets to illustrate the substantial computational benefits and superior performance of the NNGP models over other candidates and also analyze a massive United States Forest Inventory dataset to infer about the spatial distribution of forest biomass.