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Exact Bayesian inference for discretely observed Markov Jump Processes using finite rate matrices

Sherlock, Chris; Golightly, Andrew

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Authors

Chris Sherlock



Abstract

We present new methodologies for Bayesian inference on the rate parameters of a discretely observed continuous-time Markov jump process with a countably infinite statespace. The usual method of choice for inference, particle Markov chain Monte Carlo (particle MCMC), struggles when the observation noise is small. We consider the most challenging regime of exact observations and provide two new methodologies for inference in this case: the minimal extended statespace algorithm (MESA) and the nearly minimal extended statespace algorithm (nMESA). By extending the Markov chain Monte Carlo statespace, both MESA and nMESA use the exponentiation of finite rate matrices to perform exact Bayesian inference on the Markov jump process even though its statespace is countably infinite. Numerical experiments show improvements over particle MCMC of between a factor of three and several orders of magnitude.

Citation

Sherlock, C., & Golightly, A. (2023). Exact Bayesian inference for discretely observed Markov Jump Processes using finite rate matrices. Journal of Computational and Graphical Statistics, 32(1), 36-48. https://doi.org/10.1080/10618600.2022.2093886

Journal Article Type Article
Acceptance Date Jun 14, 2022
Online Publication Date Jun 29, 2022
Publication Date 2023
Deposit Date Jul 5, 2022
Publicly Available Date Mar 28, 2024
Journal Journal of Computational and Graphical Statistics
Print ISSN 1061-8600
Electronic ISSN 1537-2715
Publisher American Statistical Association
Peer Reviewed Peer Reviewed
Volume 32
Issue 1
Pages 36-48
DOI https://doi.org/10.1080/10618600.2022.2093886

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