Permutation and Grouping Methods for Sharpening Gaussian Process Approximations

Vecchia's approximate likelihood for Gaussian process parameters depends on how the observations are ordered, which has been cited as a deficiency. This article takes the alternative standpoint that the ordering can be tuned to sharpen the approximations. Indeed, the first part of the article i...

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Veröffentlicht in:Technometrics Jg. 60; H. 4; S. 415 - 429
1. Verfasser: Guinness, Joseph
Format: Journal Article
Sprache:Englisch
Veröffentlicht: United States Taylor & Francis 01.01.2018
American Society for Quality and the American Statistical Association
American Society for Quality
Schlagworte:
Accuracy
Approximation
Comparative analysis
Computation
Computer simulation
Conditional simulation
Divergence
Gaussian process
Kriging
Mathematical models
Normal distribution
Parallel computation
Partial differential equations
Permutations
Process parameters
Sharpening
Spatial-temporal data
Stochastic models
Vecchia's approximation
ISSN:0040-1706, 1537-2723
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Zusammenfassung:Vecchia's approximate likelihood for Gaussian process parameters depends on how the observations are ordered, which has been cited as a deficiency. This article takes the alternative standpoint that the ordering can be tuned to sharpen the approximations. Indeed, the first part of the article includes a systematic study of how ordering affects the accuracy of Vecchia's approximation. We demonstrate the surprising result that random orderings can give dramatically sharper approximations than default coordinate-based orderings. Additional ordering schemes are described and analyzed numerically, including orderings capable of improving on random orderings. The second contribution of this article is a new automatic method for grouping calculations of components of the approximation. The grouping methods simultaneously improve approximation accuracy and reduce computational burden. In common settings, reordering combined with grouping reduces Kullback-Leibler divergence from the target model by more than a factor of 60 compared to ungrouped approximations with default ordering. The claims are supported by theory and numerical results with comparisons to other approximations, including tapered covariances and stochastic partial differential equations. Computational details are provided, including the use of the approximations for prediction and conditional simulation. An application to space-time satellite data is presented.
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ISSN:0040-1706
1537-2723
DOI:10.1080/00401706.2018.1437476