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

Sherlock, Chris; Golightly, Andrew

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 10, 2023
• 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
• Public URL: https://durham-repository.worktribe.com/output/1202000