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An exact Gibbs sampler for the Markov‐modulated Poisson process

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  • Paul Fearnhead
  • Chris Sherlock

Abstract

Summary. A Markov‐modulated Poisson process is a Poisson process whose intensity varies according to a Markov process. We present a novel technique for simulating from the exact distribution of a continuous time Markov chain over an interval given the start and end states and the infinitesimal generator, and we use this to create a Gibbs sampler which samples from the exact distribution of the hidden Markov chain in a Markov‐modulated Poisson process. We apply the Gibbs sampler to modelling the occurrence of a rare DNA motif (the Chi site) and to inferring regions of the genome with evidence of high or low intensities for occurrences of this site.

Suggested Citation

  • Paul Fearnhead & Chris Sherlock, 2006. "An exact Gibbs sampler for the Markov‐modulated Poisson process," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(5), pages 767-784, November.
    • Handle: RePEc:bla:jorssb:v:68:y:2006:i:5:p:767-784
    DOI: 10.1111/j.1467-9868.2006.00566.x
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    Cited by:

    1. Pepa Ramírez-Cobo & Rosa Lillo & Michael Wiper, 2014. "Identifiability of the MAP 2 /G/1 queueing system," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 274-289, April.
    2. Chris Sherlock & Tatiana Xifara & Sandra Telfer & Mike Begon, 2013. "A coupled hidden Markov model for disease interactions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 62(4), pages 609-627, August.
    3. Jane M. Lange & Rebecca A. Hubbard & Lurdes Y. T. Inoue & Vladimir N. Minin, 2015. "A joint model for multistate disease processes and random informative observation times, with applications to electronic medical records data," Biometrics, The International Biometric Society, vol. 71(1), pages 90-101, March.
    4. Yera Mora, Yoel Gustavo & Lillo Rodríguez, Rosa Elvira & Ramírez-Cobo, Pepa, 2017. "Findings about the two-state BMMPP for modeling point processes in reliability and queueing systems," DES - Working Papers. Statistics and Econometrics. WS 24622, Universidad Carlos III de Madrid. Departamento de Estadística.
    5. Miasojedow, Błażej & Niemiro, Wojciech, 2016. "Geometric ergodicity of Rao and Teh’s algorithm for homogeneous Markov jump processes," Statistics & Probability Letters, Elsevier, vol. 113(C), pages 1-6.
    6. Ramírez-Cobo, Pepa & Carrizosa, Emilio & Lillo, Rosa E., 2021. "Analysis of an aggregate loss model in a Markov renewal regime," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    7. Lu Shaochuan, 2020. "Bayesian multiple changepoints detection for Markov jump processes," Computational Statistics, Springer, vol. 35(3), pages 1501-1523, September.
    8. Yera, Yoel G. & Lillo, Rosa E. & Ramírez-Cobo, Pepa, 2019. "Fitting procedure for the two-state Batch Markov modulated Poisson process," European Journal of Operational Research, Elsevier, vol. 279(1), pages 79-92.
    9. Yera, Yoel G. & Lillo, Rosa E. & Nielsen, Bo F. & Ramírez-Cobo, Pepa & Ruggeri, Fabrizio, 2021. "A bivariate two-state Markov modulated Poisson process for failure modeling," Reliability Engineering and System Safety, Elsevier, vol. 208(C).
    10. Zhou, Jie & Song, Xinyuan & Sun, Liuquan, 2020. "Continuous time hidden Markov model for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    11. Landon, Joshua & Özekici, Süleyman & Soyer, Refik, 2013. "A Markov modulated Poisson model for software reliability," European Journal of Operational Research, Elsevier, vol. 229(2), pages 404-410.
    12. Ramírez Cobo, Josefa & Lillo Rodríguez, Rosa Elvira & Wiper, Michael Peter, 2009. "Non-identifiability of the two state Markovian Arrival process," DES - Working Papers. Statistics and Econometrics. WS ws097121, Universidad Carlos III de Madrid. Departamento de Estadística.

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