Statistical Inference for Spatiotemporal Partially Observed Markov Processes via the R Package spatPomp

Abstract

We consider inference for a class of nonlinear stochastic processes with latent dynamic variables and spatial structure. The spatial structure takes the form of a finite collection of spatial units that are dynamically coupled. We assume that the latent processes have a Markovian structure and that unit-specific noisy measurements are made. A model of this form is called a spatiotemporal partially observed Markov process (SpatPOMP). The R package spatPomp provides an environment for implementing SpatPOMP models, analyzing data, and developing new inference approaches. We describe the spatPomp implementations of some methods with scaling properties suited to SpatPOMP models. We demonstrate the package on a simple Gaussian system and on a nontrivial epidemiological model for measles transmission within and between cities. We show how to construct user-specified SpatPOMP models within spatPomp