Nearest-Neighbor Gaussian Process Models for Bayesian Inference on Large Spatio-Temporal Data

• Activity Number: 6
• Type: Invited
• Date/Time: Sunday, August 9, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Sudipto Banerjee* and Abhirup Datta and Andrew O. Finley
• Companies: UCLA and University of Minnesota and Michigan State University
• Keywords: Bayesian inference ; Gaussian processes ; Nearest-neighbor models ; Non-separable covariances ; Sparsity ; Spatiotemporal residual

Abstract

Spatially-temporally oriented data are widely encountered in the physical and engineering sciences. Popular Gaussian process models for such data are computationally prohibitive if the number of space-time coordinates is large. We construct a highly scalable Nearest Neighbor Gaussian Process (NNGP) to enable fully model-based inference for large spatiotemporal data. The NNGP is a well-defined spatial process providing legitimate finite-dimensional Gaussian densities with sparse precision matrices. Every Gaussian process model, univariate or multivariate, produces a family of highly scalable NNGP model. We embed the NNGP as a sparsity-inducing prior within a Bayesian setting that delivers full inference efficiently without storing or factorizing large matrices. The floating point operations (flops) per iteration of this algorithm is linear in the number of spatial locations, thereby rendering massive scalability. We illustrate the computational and inferential benefits of the NNGP over competing methods using simulation studies and also analyze forest biomass from a massive United States Forest Inventory dataset at a scale that precludes alternative dimension-reducing methods.