Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets

Spatial process models for analyzing geostatistical data entail computations that become prohibitive as the number of spatial locations become large. This article develops a class of highly scalable nearest-neighbor Gaussian process (NNGP) models to provide fully model-based inference for large geos...

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Bibliographic Details
Published in:Journal of the American Statistical Association 2016-06, Vol.111 (514), p.800-812
Main Authors: Datta, Abhirup, Banerjee, Sudipto, Finley, Andrew O., Gelfand, Alan E.
Format: Article
Language:English
Subjects:
Algorithms
Bayesian modeling
Gaussian process
Geostatistics
Hierarchical models
Markov analysis
Markov chain Monte Carlo
Monte Carlo simulation
Nearest neighbors
Normal distribution
Predictive process
Reduced-rank models
Simulation
Sparse precision matrices
Spatial cross-covariance functions
Statistics
Theory and Methods
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Summary:Spatial process models for analyzing geostatistical data entail computations that become prohibitive as the number of spatial locations become large. This article develops a class of highly scalable nearest-neighbor Gaussian process (NNGP) models to provide fully model-based inference for large geostatistical datasets. We establish that the NNGP is a well-defined spatial process providing legitimate finite-dimensional Gaussian densities with sparse precision matrices. We embed the NNGP as a sparsity-inducing prior within a rich hierarchical modeling framework and outline how computationally efficient Markov chain Monte Carlo (MCMC) algorithms can be executed without storing or decomposing large matrices. The floating point operations (flops) per iteration of this algorithm is linear in the number of spatial locations, thereby rendering substantial scalability. We illustrate the computational and inferential benefits of the NNGP over competing methods using simulation studies and also analyze forest biomass from a massive U.S. Forest Inventory dataset at a scale that precludes alternative dimension-reducing methods. Supplementary materials for this article are available online.
ISSN:0162-1459
1537-274X
DOI:10.1080/01621459.2015.1044091