Conjugate Bayesian Multivariate Spatial Models with Accelerated Posterior Sampling Using Conjugate Gradient Method

• Activity Number: 254 - Contributed Poster Presentations: Section on Bayesian Statistical Science
• Type: Contributed
• Date/Time: Monday, July 29, 2019 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Lu Zhang* and Sudipto Banerjee
• Companies: UCLA Biostatistics and UCLA
• Keywords: Conjugate Gradient; Nearest-Neighbor Gaussian Process; Conjugate Bayesian Modeling; Big Data

Abstract

The BIG DATA problem in multivariate geostatistics has fomented a rich literature on scalable methodologies for analyzing multivariate large spatial datasets. The scalable spatial process models within the Bayesian paradigm have been found especially attractive due to their flexibility and presence in hierarchical model settings. However, a major computational bottleneck for obtaining full Bayesian inference, including the inference for latent processes, arises from the slow MCMC sampling process over a high-dimensional parameter space. This article devises some simple massively scalable Bayesian models that can rapidly deliver full Bayesian inference on multivariate spatial processes that are practically indistinguishable from inference obtained using more expensive alternatives. One key strategy we develop uses the conjugate gradient method to accelerate the posterior sampling process of Nearest-Neighbor Gaussian process models within a conjugate Bayesian paradigm. We demonstrate our methods on real and synthetic geostatistical data sets and show how massive datasets with observations in the millions can be analyzed on modest laptops.