Model-based Inference

ICTP Workshop on Mathematical Models of Climate Variability, Environmental Change and Infectious Diseases

Important Note: Some of these materials have been updated for use with version 2.8. As of version 2, pomp syntax has changed substantially. These changes are documented on the pomp website.

Some of the materials have been superseded entirely. In these cases, links are provided to the updated material.

---

Instructor

Prof. Aaron A. King,
Ph.D. Departments of Ecology & Evolutionary Biology and Mathematics
University of Michigan
Email: kingaaictp5@gmail.com

---

Preparing for the workshop

1. Complete the R tutorial before the beginning of the course.
2. If you wish to use your own computer, install R and RStudio on it before the first day of the course. Instructions for doing so are here.

---

Topics

• Ordinary differential equation models in pomp
• Introduction to inference
• Brief introduction to likelihood
• Simulation of stochastic processes by Euler’s method
• Simulation of stochastic processes by Gillespie’s method
• Introduction to partially observed Markov processes
• Likelihood for POMP models
• Iterated filtering: principles and practice

---

Readings

The following papers serve as background for some of the central issues:

• S. N. Wood (2010) Statistical inference for noisy nonlinear ecological dynamic systems. Nature, 466: 1102–1104. DOI: 10.1038/nature09319.
• A. A. King, E. L. Ionides, M. Pascual, and M. J. Bouma (2008) Inapparent infections and cholera dynamics. Nature, 454: 877–880. DOI: 10.1038/nature07084
• S. Shrestha, A. A. King, and P. Rohani (2011) Statistical Inference for Multi-Pathogen Systems. PLoS Comput. Biol., 7: e1002135. DOI: 10.1371/journal.pcbi.1002135

A good reference for modeling in infectious disease epidemiology is:

• Keeling, M. & Rohani, P. Modeling infectious diseases in humans and animals. Princeton University Press, 2008.

The pomp package is described and illustrated in

• A. A. King, D. Nguyen, and E. L. Ionides (2016) Statistical Inference for Partially Observed Markov Processes via the R Package pomp. J. Stat. Soft., 69: 1–43. DOI: 10.18637/jss.v069.i12

---

Links

• R Tutorial
  
• Tutorial on data munging with plyr, reshape2, and magrittr
  
• Tutorial on ggplot2
  
• Source code for these notes
  
• pomp homepage

---

License

CC-BY-NC

This work is licensed under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).

• Under its terms, you are free to:
  • Share — copy and redistribute the material in any medium or format
  • Adapt — remix, transform, and build upon the material The licensor cannot revoke these freedoms as long as you follow the license terms.
• Under the following terms:
  • Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • Non-Commercial — You may not use the material for commercial purposes.
  • No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
• Notices:
  • You do not have to comply with the license for elements of the material in the public domain or where your use is permitted by an applicable exception or limitation.
  • No warranties are given. The license may not give you all of the permissions necessary for your intended use. For example, other rights such as publicity, privacy, or moral rights may limit how you use the material.

---