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

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  • King, Aaron A.
  • Nguyen, Dao
  • Ionides, Edward L.

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.

Suggested Citation

  • King, Aaron A. & Nguyen, Dao & Ionides, Edward L., 2016. "Statistical Inference for Partially Observed Markov Processes via the R Package pomp," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 69(i12).
    • Handle: RePEc:jss:jstsof:v:069:i12
    DOI: http://hdl.handle.net/10.18637/jss.v069.i12
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    References listed on IDEAS

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    1. Lux, Thomas, 2022. "Inference for Nonlinear State Space Models: A Comparison of Different Methods applied to Markov-Switching Multifractal Models," Econometrics and Statistics, Elsevier, vol. 21(C), pages 69-95.
    2. Maria Masotti & Lin Zhang & Ethan Leng & Gregory J. Metzger & Joseph S. Koopmeiners, 2023. "A novel Bayesian functional spatial partitioning method with application to prostate cancer lesion detection using MRI," Biometrics, The International Biometric Society, vol. 79(2), pages 604-615, June.
    3. Oscar García, 2019. "Estimating reducible stochastic differential equations by conversion to a least-squares problem," Computational Statistics, Springer, vol. 34(1), pages 23-46, March.
    4. Driver, Charles C. & Oud, Johan H. L. & Voelkle, Manuel C., 2017. "Continuous Time Structural Equation Modeling with R Package ctsem," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 77(i05).
    5. Jonathan Fintzi & Jon Wakefield & Vladimir N. Minin, 2022. "A linear noise approximation for stochastic epidemic models fit to partially observed incidence counts," Biometrics, The International Biometric Society, vol. 78(4), pages 1530-1541, December.
    6. Johannes Bracher & Leonhard Held, 2021. "A marginal moment matching approach for fitting endemic‐epidemic models to underreported disease surveillance counts," Biometrics, The International Biometric Society, vol. 77(4), pages 1202-1214, December.
    7. Heather Williams & Andrew Scharf & Anna R. Ryba & D. Ryan Norris & Daniel J. Mennill & Amy E. M. Newman & Stéphanie M. Doucet & Julie C. Blackwood, 2022. "Cumulative cultural evolution and mechanisms for cultural selection in wild bird songs," Nature Communications, Nature, vol. 13(1), pages 1-11, December.
    8. King, Aaron A. & Lin, Qianying & Ionides, Edward L., 2022. "Markov genealogy processes," Theoretical Population Biology, Elsevier, vol. 143(C), pages 77-91.
    9. Lawrence W Sheppard & Emma J Defriez & Philip C Reid & Daniel C Reuman, 2019. "Synchrony is more than its top-down and climatic parts: interacting Moran effects on phytoplankton in British seas," PLOS Computational Biology, Public Library of Science, vol. 15(3), pages 1-25, March.
    10. Tobias S Brett & Eamon B O’Dea & Éric Marty & Paige B Miller & Andrew W Park & John M Drake & Pejman Rohani, 2018. "Anticipating epidemic transitions with imperfect data," PLOS Computational Biology, Public Library of Science, vol. 14(6), pages 1-18, June.
    11. Lux, Thomas, 2018. "Inference for nonlinear state space models: A comparison of different methods applied to Markov-switching multifractal models," Economics Working Papers 2018-07, Christian-Albrechts-University of Kiel, Department of Economics.
    12. Quentin Clairon & Adeline Samson, 2020. "Optimal control for estimation in partially observed elliptic and hypoelliptic linear stochastic differential equations," Statistical Inference for Stochastic Processes, Springer, vol. 23(1), pages 105-127, April.
    13. Michael Briga & Elizabeth Goult & Tobias S. Brett & Pejman Rohani & Matthieu Domenech de Cellès, 2024. "Maternal pertussis immunization and the blunting of routine vaccine effectiveness: a meta-analysis and modeling study," Nature Communications, Nature, vol. 15(1), pages 1-11, December.

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