Spatiotemporal statistics

Overview

Developing spatial and spatiotemporal models using stochastic partial differential equations

Spatiotemporal modeling Basic generalized linear mixed effects models can account for spatial (and spatiotemporal) autocorrelation using latent Gaussian random fields (GRFs). However, GRFs are computationally intense due to costly covariance functions. Stochastic Partial Differential Equations (SPDE) can be used to minimize the scale of this problem by approximating GRFs with Gaussian Markcov random fields (GMRFs) with a Matern covariance function (Lindgrin et al., 2011; Krainski et al. 2018). This solution has been adopted by the Integrated Nested Laplace Approximation (INLA) software, and has later been implimented in Template Model Builder (TMB) software (Thorson et al., 2015).

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