spatPomp: An R package for spatiotemporal partially observed Markov process models

Kidus Asfaw, Joonha Park, Aaron A. King, Edward Ionides

Abstract:

The development of spatPomp was motivated by the goal of investigating dynamics arising from
a collection of spatially distributed, interacting biological populations. The entire population,
consisting of the union of these sub-populations over all the spatial locations, is called a
metapopulation. Each sub-population may have its own structure, which could correspond to
disease status in an epidemiological model or abundance of several species in an ecosystem
model. The spatPomp package embeds this goal in a more general problem: inference for
spatiotemporal partially observed Markov process (SpatPOMP) models. A POMP model
consists of a latent Markov process model, together with a measurement model describing
how the data arise from noisy and/or incomplete observation of this latent state. The latent
Markov process may be constructed in discrete or continuous time, taking scalar or vector
values in a discrete or continuous space. POMP models are also known as state space models,
or hidden Markov models. A SpatPOMP model extends the POMP model formulation by
adding an index set corresponding to spatial location, so that the state of the SpatPOMP
is comprised of a value for each location. We say “unit” rather than “spatial location” to
build our framework in the general context of an arbitrary index set. Measurements are made
on each unit, and are assumed to depend only on the latent state value for that unit. The
spatPomp R package provides a computational framework for modeling and statistical inference
on SpatPOMP models.