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

2019/12/16 by Chris Sherlock, Sherlock, Chris, Andrew Golightly +1
Mathematics · #62F15 #Computation (stat.CO) #FOS: Computer and information sciences #Markov Chains and Monte Carlo Methods #Methodology (stat.ME) #Other Statistics (stat.OT) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.2001.02168

openalex publication_date 2019/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present new methodologies for Bayesian inference on the rate parameters of a discretely observed continuous-time Markov jump processes with a countably infinite state space. 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 state space algorithm (MESA) and the nearly minimal extended state space algorithm (nMESA). By extending the Markov chain Monte Carlo state space, both MESA and nMESA use the exponentiation of finite rate matrices to perform exact Bayesian inference on the Markov jump process even though its state space is countably infinite. Numerical experiments show improvements over particle MCMC of between a factor of three and several orders of magnitude.

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