Efficient sampling of conditioned Markov jump processes

• Published in: Statistics and computing Vol. 29; no. 5; pp. 1149 - 1163
• Main Authors: Golightly, Andrew, Sherlock, Chris
• Format: Journal Article
• Language: English
• Published: New York Springer US 11.09.2019; Springer Nature B.V
• Subjects: Algorithms; Approximation; Artificial Intelligence; Bridges; Computer simulation; Conditioning; Markov analysis; Markov chains; Mathematical analysis; Mathematics and Statistics; Monte Carlo simulation; Probability and Statistics in Computer Science; Resampling; Statistical Theory and Methods; Statistics; Statistics and Computing/Statistics Programs; Conditioned hazard; Linear noise approximation; Chemical Langevin equation; Markov jump process
• ISSN: 0960-3174; 1573-1375
• DOI: 10.1007/s11222-019-09861-5

We consider the task of generating draws from a Markov jump process (MJP) between two time points at which the process is known. Resulting draws are typically termed bridges , and the generation of such bridges plays a key role in simulation-based inference algorithms for MJPs. The problem is challenging due to the intractability of the conditioned process, necessitating the use of computationally intensive methods such as weighted resampling or Markov chain Monte Carlo. An efficient implementation of such schemes requires an approximation of the intractable conditioned hazard/propensity function that is both cheap and accurate. In this paper, we review some existing approaches to this problem before outlining our novel contribution. Essentially, we leverage the tractability of a Gaussian approximation of the MJP and suggest a computationally efficient implementation of the resulting conditioned hazard approximation. We compare and contrast our approach with existing methods using three examples.