spate: An R Package for Spatio-Temporal Modeling with a Stochastic Advection-Diffusion Process

Fabio Sigrist, Hans R. Künsch, Werner A. Stahel

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The R package spate implements methodology for modeling of large space-time data sets. A spatio-temporal Gaussian process is defined through a stochastic partial differential equation (SPDE) which is solved using spectral methods. In contrast to the traditional geostatistical way of relying on the covariance function, the spectral SPDE approach is computationally tractable and provides a realistic space-time parametrization.
This package aims at providing tools for simulating and modeling of spatio-temporal processes using an SPDE based approach. The package contains functions for obtaining parametrizations, such as propagator or innovation covariance matrices, of the spatio-temporal model. This allows for building customized hierarchical Bayesian models using the SPDE based model at the process stage. The functions of the package then provide computationally efficient algorithms needed for doing inference with the hierarchical model. Furthermore, an adaptive Markov chain Monte Carlo (MCMC) algorithm implemented in the package can be used as an algorithm for doing inference without any additional modeling. This function is flexible and allows for application specific customizing. The MCMC algorithm supports data that follow a Gaussian or a censored distribution with point mass at zero. Spatio-temporal covariates can be included in the model through a regression term.

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