Statistical Inference for Partially Observed Markov Processes via the R Package pomp

TL;DR

The paper introduces the R package pomp, which offers a flexible framework for statistical inference in partially observed Markov process models, enabling various modern methods and complex model specifications.

Contribution

It presents the implementation of multiple advanced statistical methods for POMP models within the pomp package and demonstrates their application to both simple and complex real-world models.

Findings

Successful application of methods to toy problems

Demonstration of complex epidemiological model specification

Discussion of extending the package with new methods

Abstract

Partially observed Markov process (POMP) models, also known as hidden Markov models or state space models, are ubiquitous tools for time series analysis. The R package pomp provides a very flexible framework for Monte Carlo statistical investigations using nonlinear, non-Gaussian POMP models. A range of modern statistical methods for POMP models have been implemented in this framework including sequential Monte Carlo, iterated filtering, particle Markov chain Monte Carlo, approximate Bayesian computation, maximum synthetic likelihood estimation, nonlinear forecasting, and trajectory matching. In this paper, we demonstrate the application of these methodologies using some simple toy problems. We also illustrate the specification of more complex POMP models, using a nonlinear epidemiological model with a discrete population, seasonality, and extra-demographic stochasticity. We discuss the specification of user-defined models and the development of additional methods within the programming environment provided by pomp.