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Exact filtering for partially observed continuous time models

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  • Paul Fearnhead
  • Loukia Meligkotsidou

Abstract

Summary. The forward–backward algorithm is an exact filtering algorithm which can efficiently calculate likelihoods, and which can be used to simulate from posterior distributions. Using a simple result which relates gamma random variables with different rates, we show how the forward–backward algorithm can be used to calculate the distribution of a sum of gamma random variables, and to simulate from their joint distribution given their sum. One application is to calculating the density of the time of a specific event in a Markov process, as this time is the sum of exponentially distributed interevent times. This enables us to apply the forward–backward algorithm to a range of new problems. We demonstrate our method on three problems: calculating likelihoods and simulating allele frequencies under a non‐neutral population genetic model, analysing a stochastic epidemic model and simulating speciation times in phylogenetics.

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  • Paul Fearnhead & Loukia Meligkotsidou, 2004. "Exact filtering for partially observed continuous time models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(3), pages 771-789, August.
    • Handle: RePEc:bla:jorssb:v:66:y:2004:i:3:p:771-789
    DOI: 10.1111/j.1467-9868.2004.05561.x
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    Cited by:

    1. McKinley, Trevelyan J. & Ross, Joshua V. & Deardon, Rob & Cook, Alex R., 2014. "Simulation-based Bayesian inference for epidemic models," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 434-447.
    2. Paas, L.J. & Vermunt, J.K. & Bijmolt, T.H.A., 2007. "Discrete-time discrete-state latent Markov modelling for assessing and predicting household acquisitions of financial products," Other publications TiSEM 5781ab33-6687-4ad5-b57a-3, Tilburg University, School of Economics and Management.
    3. Wouterse, Bram & Huisman, Martijn & Meijboom, Bert R. & Deeg, Dorly J.H. & Polder, Johan J., 2013. "Modeling the relationship between health and health care expenditures using a latent Markov model," Journal of Health Economics, Elsevier, vol. 32(2), pages 423-439.
    4. Phenyo E. Lekone & Bärbel F. Finkenstädt, 2006. "Statistical Inference in a Stochastic Epidemic SEIR Model with Control Intervention: Ebola as a Case Study," Biometrics, The International Biometric Society, vol. 62(4), pages 1170-1177, December.
    5. Leonard J. Paas & Jeroen K. Vermunt & Tammo H. A. Bijmolt, 2007. "Discrete time, discrete state latent Markov modelling for assessing and predicting household acquisitions of financial products," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(4), pages 955-974, October.
    6. Meligkotsidou, Loukia & Tzavalis, Elias & Vrontos, Ioannis, 2017. "On Bayesian analysis and unit root testing for autoregressive models in the presence of multiple structural breaks," Econometrics and Statistics, Elsevier, vol. 4(C), pages 70-90.

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