On nearest-neighbor Gaussian process models for massive spatial data

Gaussian Process (GP) models provide a very flexible nonparametric approach to modeling location‐and‐time indexed datasets. However, the storage and computational requirements for GP models are infeasible for large spatial datasets. Nearest Neighbor Gaussian Processes (Datta A, Banerjee S, Finley AO...

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Bibliographic Details
Published in:Wiley interdisciplinary reviews. Computational statistics 2016-09, Vol.8 (5), p.162-171
Main Authors: Datta, Abhirup, Banerjee, Sudipto, Finley, Andrew O., Gelfand, Alan E.
Format: Article
Language:English
Subjects:
Bayesian analysis
Bayesian methods and theory
Computation
computational Bayesian methods
Computer applications
Covariance matrix
Data
Data analysis
Data processing
data structures
Datasets
Equivalence
Gaussian
Gaussian process
Geostatistics
Graphical methods
image and spatial data
Kriging interpolation
Mathematical models
Modelling
Multivariate analysis
Probability theory
Spatial data
Specifications
Statistical methods
Statistics
Storage
Wire
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Summary:Gaussian Process (GP) models provide a very flexible nonparametric approach to modeling location‐and‐time indexed datasets. However, the storage and computational requirements for GP models are infeasible for large spatial datasets. Nearest Neighbor Gaussian Processes (Datta A, Banerjee S, Finley AO, Gelfand AE. Hierarchical nearest‐neighbor gaussian process models for large geostatistical datasets. J Am Stat Assoc 2016., JASA) provide a scalable alternative by using local information from few nearest neighbors. Scalability is achieved by using the neighbor sets in a conditional specification of the model. We show how this is equivalent to sparse modeling of Cholesky factors of large covariance matrices. We also discuss a general approach to construct scalable Gaussian Processes using sparse local kriging. We present a multivariate data analysis which demonstrates how the nearest neighbor approach yields inference indistinguishable from the full rank GP despite being several times faster. Finally, we also propose a variant of the NNGP model for automating the selection of the neighbor set size. WIREs Comput Stat 2016, 8:162–171. doi: 10.1002/wics.1383 This article is categorized under: Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory Data: Types and Structure > Image and Spatial Data
ISSN:1939-5108
1939-0068
DOI:10.1002/wics.1383