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This document was produced using pomp2 version 2.0.13.1 and R version 3.5.3.

Introduction

This tutorial aims to help you get started using pomp2 as a suite of tools for analysis of time series data based on stochastic dynamical systems models. First, we give some conceptual background regarding the class of models—partially observed Markov processes (POMPs)—that pomp2 handles. We then discuss some preliminaries: installing the package and so on. Next, we show how to simulate a POMP using pomp2. We then analyze some data using a few different tools. In so doing, we illustrate some of the package’s capabilities by using its algorithms to fit, compare, and criticize the models using pomp2’s algorithms. From time to time, exercises for the reader are given.

Partially observed Markov process (POMP) models

Structure of a POMP

As its name implies pomp2 is focused on partially observed Markov process models. These are also known as state-space models, hidden Markov models, and stochastic dynamical systems models. Such models consist of an unobserved Markov state process, connected to the data via an explicit model of the observation process. We refer to the former as the latent process model (or process model for short) and the latter as the measurement model.

Mathematically, each model is a probability distribution. Let \(Y_n\) denote the measurement process and \(X_n\) the latent state process, then by definition, the process model is determined by the density \(f_{X_n|X_{n-1}}\) and the initial density \(f_{X_0}\). The measurement process is determined by the density \(f_{Y_n|X_n}\). These two submodels determine the full POMP model, i.e., the joint distribution \(f_{X_{0:N},Y_{1:N}}\). If we have a sequence of measurements, \(y^*_{n}\), made at times \(t_n\), \(n=1,\dots,N\), then we think of these data, collectively, as a single realization of the