Modeling spatial data using local likelihood estimation and a Matérn to spatial autoregressive translation

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 Matern 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.