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Modeling spatial data using local likelihood estimation and a Matérn to spatial autoregressive translation
Author(s) -
Wiens Ashton,
Nychka Douglas,
Kleiber William
Publication year - 2020
Publication title -
environmetrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.68
H-Index - 58
eISSN - 1099-095X
pISSN - 1180-4009
DOI - 10.1002/env.2652
Subject(s) - covariance , autoregressive model , covariance function , random field , kriging , computer science , gaussian , gaussian process , algorithm , spatial analysis , matérn covariance function , mathematics , statistics , covariance intersection , physics , quantum mechanics
Modeling data with nonstationary covariance structure is important to represent heterogeneity in geophysical and other environmental spatial processes. In this work, we investigate a two‐stage approach to modeling nonstationary covariances that is efficient for large data sets. First, maximum likelihood estimation is used in local, moving windows to infer spatially varying covariance parameters. These surfaces of covariance parameters are then encoded into a global covariance model specifying the second‐order structure for the complete spatial domain. From this second step, the resulting global model allows for efficient simulation and prediction. This work uses a nonstationary spatial autoregressive (SAR) model, related to Gaussian Markov random field methods, as the global model which is amenable to plug in local estimates and practical for large datasets. A simulation study is used to establish the accuracy of local Matérn parameter estimation as a reliable technique for small window sizes and a modest number of replicated fields. This modeling approach is implemented on a nonstationary climate model dataset with the goal of emulating the variation in the numerical model ensemble using a Gaussian process.