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Bayesian modeling for large spatial datasets

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We focus upon flexible Bayesian hierarchical models for scientific data available at geo‐coded locations. Investigators are increasingly turning to spatial process models to analyze such datasets. These models are customarily estimated using Markov Chain Monte Carlo (MCMC) methods, which have become especially popular for spatial modeling, given their flexibility and power to fit models that would be infeasible otherwise. However, estimating Bayesian spatial process models is undermined by prohibitive computational expenses associated with parameter estimation. Classes of low‐rank spatial process models are increasingly being deployed to resolve this problem by projecting spatial effects to a lower‐dimensional subspace. We discuss how a low‐rank process called the ‘predictive process’ seamlessly enters the hierarchical modeling framework and helps us accrue substantial computational benefits. WIREs Comp Stat 2012, 4:59–66. doi: 10.1002/wics.187

Figure 1.

Forest biomass dataset and associated estimates for the 50 knot predictive process models: (a) location of forest inventory plots; (b) interpolated surface of the nonspatial model residuals; and (c) predictive process model estimated spatial random effects with knot locations.

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Data Structures > Image and Spatial Data
Computational Bayesian Methods > Markov Chain Monte Carlo (MCMC)
Computational Bayesian Methods > Bayesian Methods and Theory
Machine Learning > Statistical Methodology

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