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Title: A divide-and-conquer Bayesian approach to large-scale kriging Authors:  Rajarshi Guhaniyogi - University of California Santa Cruz (United States)
Cheng Li - National University of Singapore (Singapore) [presenting]
Terrance Savitsky - US Bureau of Labor Statistics (United States)
Sanvesh Srivastava - The University of Iowa (United States)
Abstract: Flexible hierarchical Bayesian modeling of massive data is challenging due to poorly scaling computations in large sample size settings. The motivation comes from spatial process models for analyzing geostatistical data, which typically entail computations that become prohibitive as the number of spatial locations becomes large. We propose a three-step divide-and-conquer strategy within the Bayesian paradigm to achieve massive scalability for any spatial process model. We partition the data into a large number of subsets, apply a readily available spatial process model on every subset in parallel, and optimally combine the posterior distributions estimated on all the subsets into a pseudo posterior distribution that is used for predictive and parametric inference and residual surface interpolation. We call this approach ``Distributed Kriging'' (DISK). The Bayes risk of estimating the true residual spatial surface using the DISK posterior distribution decays to zero at a nearly optimal rate under mild assumptions. While DISK is a general approach to divide-and-conquer Bayesian nonparametric regression, we focus on its applications in spatial statistics and demonstrate its empirical performance using models based on stationary full-rank and nonstationary low-rank Gaussian process priors. A variety of simulations and a geostatistical analysis of the Pacific Ocean sea surface temperature data validate our theoretical results.