Practical Bayesian inference based on Nearest Neighbor Gaussian Processes (NNGP) model for massive spatial data

• Activity Number: 625 - Environmental Epidemiology and Spatial Statistics
• Type: Contributed
• Date/Time: Thursday, August 3, 2017 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Lu Zhang* and Abhirup Datta and Sudipto Banerjee
• Companies: UCLA and Johns Hopkins University and UCLA Fielding School of Public Health
• Keywords: Nearest-Neighbor Gaussian Processes ; Hamiltonian Monte Carlo ; high-dimensional geostatistics

Abstract

Gaussian Process (GP) models provide a versatile nonparametric modeling method to model spatial datasets. However, the implementation of GP models entails storage and computation requirement that become prohibitive as the number of spatial locations becomes large. Moreover, long run-times often occur for estimating parameters due to the inefficiency of Markov Chain Monte Carlo (MCMC) algorithms and irregular of the posterior surface of the parameters. In this work, we propose a highly efficient algorithm for obtaining Bayesian inference in analyzing large-scale irregular spatial data, which unites the strength of scalable models based upon recently proposed Nearest-Neighbor Gaussian Processes (NNGP) and conjugate gradient method. We show that sampling from the conjugate NNGP random effects model with conjugate gradient method dramatically increases the sampling efficiency and reduces the computational burden.We demonstrate our methods on synthetic geostatistical data sets and an application on mapping sea surface temperature over eastern Pacific.