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On the estimation of partially observed continuous-time Markov chains

Author

Listed:
  • Alan Riva-Palacio

    (IIMAS, UNAM)

  • Ramsés H. Mena

    (IIMAS, UNAM)

  • Stephen G. Walker

    (University of Texas at Austin)

Abstract

Motivated by the increasing use of discrete-state Markov processes across applied disciplines, a Metropolis–Hastings sampling algorithm is proposed for a partially observed process. Current approaches, both classical and Bayesian, have relied on imputing the missing parts of the process and working with a complete likelihood. However, from a Bayesian perspective, the use of latent variables is not necessary and exploiting the observed likelihood function, combined with a suitable Markov chain Monte Carlo method, results in an accurate and efficient approach. A comprehensive comparison with simulated and real data sets demonstrate our approach when compared with alternatives available in the literature.

Suggested Citation

  • Alan Riva-Palacio & Ramsés H. Mena & Stephen G. Walker, 2023. "On the estimation of partially observed continuous-time Markov chains," Computational Statistics, Springer, vol. 38(3), pages 1357-1389, September.
    • Handle: RePEc:spr:compst:v:38:y:2023:i:3:d:10.1007_s00180-022-01273-w
    DOI: 10.1007/s00180-022-01273-w
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    References listed on IDEAS

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    1. Mogens Bladt & Michael Sørensen, 2005. "Statistical inference for discretely observed Markov jump processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(3), pages 395-410, June.
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    5. Yasunari Inamura, 2006. "Estimating Continuous Time Transition Matrices From Discretely Observed Data," Bank of Japan Working Paper Series 06-E-7, Bank of Japan.
    6. Ruben Amoros & Ruth King & Hidenori Toyoda & Takashi Kumada & Philip J. Johnson & Thomas G. Bird, 2019. "A continuous-time hidden Markov model for cancer surveillance using serum biomarkers with application to hepatocellular carcinoma," METRON, Springer;Sapienza Università di Roma, vol. 77(2), pages 67-86, August.
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