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**Note:** This document has been updated for **pomp** version 2.

Produced in **R** version 4.0.2 using **pomp** version 3.1.1.0.

## Partially observed Markov process (POMP) models

Data \(y^*_1,\dots,y^*_N\) collected at times \(t_1<\dots<t_N\) are modeled as noisy, incomplete, and indirect observations of a Markov process \(\{X(t), t\ge t_0\}\).

This is a **partially observed Markov process (POMP)** model, also known as a hidden Markov model or a state space model.

- The POMP class of models can accommodate a variety of complexities that commonly arise, especially in biological models:
- latent variables
- nonlinear dynamics
- non-Gaussian distributions
- continuous-time models (as well as discrete-time models)
- intractable likelihoods
- non-differentiable models

## Goals

The **R** package **pomp** provides

- facilities for modeling POMPs,
- a toolbox of statistical inference methods for analyzing data using POMPs, and
- a development platform for implementing new POMP inference methods.

The goals of the **pomp** project are to:

- facilitate scientific progress by providing high quality, general purpose, reproducible algorithms for statistical inference on POMPs.
- help separate model issues from method issues to allow one to accurately distinguish model failure from method failure, method improvement from model improvement, etc.
- provide a test-bed for the development and implementation of new inference algorithms by simplifying the model interface and providing a plethora of benchmarks.
- exploit potential synergies afforded by hybrid approaches and cross-fertilization of ideas.

Our goal in this presentation is two-fold:

To demonstrate and explain the package...

- ...from the point of view of the user interested in application of the included methods to a specific data analysis based on a specific set of models.
- ...from the point of view of a methods developer, who wishes to exploit the package's structure write new methods in such a way that they can be applied to a POMP models generally.

#### Notation for partially observed Markov process models