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Markov genealogy processes

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  • King, Aaron A.
  • Lin, Qianying
  • Ionides, Edward L.

Abstract

We construct a family of genealogy-valued Markov processes that are induced by a continuous-time Markov population process. We derive exact expressions for the likelihood of a given genealogy conditional on the history of the underlying population process. These lead to a nonlinear filtering equation which can be used to design efficient Monte Carlo inference algorithms. We demonstrate these calculations with several examples. Existing full-information approaches for phylodynamic inference are special cases of the theory.

Suggested Citation

  • King, Aaron A. & Lin, Qianying & Ionides, Edward L., 2022. "Markov genealogy processes," Theoretical Population Biology, Elsevier, vol. 143(C), pages 77-91.
    • Handle: RePEc:eee:thpobi:v:143:y:2022:i:c:p:77-91
    DOI: 10.1016/j.tpb.2021.11.003
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    References listed on IDEAS

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    1. Bretó, Carles & Ionides, Edward L., 2011. "Compound Markov counting processes and their applications to modeling infinitesimally over-dispersed systems," DES - Working Papers. Statistics and Econometrics. WS ws111914, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Bretó, Carles & Ionides, Edward L., 2011. "Compound Markov counting processes and their applications to modeling infinitesimally over-dispersed systems," Stochastic Processes and their Applications, Elsevier, vol. 121(11), pages 2571-2591, November.
    3. David A Rasmussen & Oliver Ratmann & Katia Koelle, 2011. "Inference for Nonlinear Epidemiological Models Using Genealogies and Time Series," PLOS Computational Biology, Public Library of Science, vol. 7(8), pages 1-11, August.
    4. J. O. Lloyd-Smith & S. J. Schreiber & P. E. Kopp & W. M. Getz, 2005. "Superspreading and the effect of individual variation on disease emergence," Nature, Nature, vol. 438(7066), pages 355-359, November.
    5. Manon Ragonnet-Cronin & Olivia Boyd & Lily Geidelberg & David Jorgensen & Fabricia F. Nascimento & Igor Siveroni & Robert A. Johnson & Marc Baguelin & Zulma M. Cucunubá & Elita Jauneikaite & Swapnil M, 2021. "Genetic evidence for the association between COVID-19 epidemic severity and timing of non-pharmaceutical interventions," Nature Communications, Nature, vol. 12(1), pages 1-7, December.
    6. Simon N. Wood, 2010. "Statistical inference for noisy nonlinear ecological dynamic systems," Nature, Nature, vol. 466(7310), pages 1102-1104, August.
    7. 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).
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