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Abstract:
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Flexible hierarchical Bayesian modeling of massive data is challenging due to poorly scaling computations in large sample size settings. This talk will focus on spatial/spatio-temporal process models for analyzing geostatistical data, which typically entail computations that become prohibitive as the number of spatial locations and/or time points becomes large. We propose a three-step divide-and-conquer strategy within the Bayesian paradigm to achieve massive scalability for any spatial/spatio-temporal process model. We partition the data into a large number of subsets, apply a readily available Bayesian spatial/spatio-temporal process model on every subset in parallel, and optimally combine the posterior distributions estimated across all the subsets into a pseudo-posterior distribution that conditions on the entire data. The combined pseudo posterior distribution is used for predicting the responses at arbitrary locations and for performing posterior inference on the model parameters and the residual spatial surface. This approach offers significant advantages in applications where the entire data are or can be stored on multiple machines. Under the standard theoretical setup, we show that if the number of subsets is not too large, then the Bayes risk of estimating the true residual spatial surface using the pseudo posterior distribution decays to zero at a nearly optimal rate. A variety of simulations and a geostatistical analysis of the Pacific Ocean sea surface temperature data validate our theoretical results.
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