Efficient sampling of conditioned Markov jump processes

TL;DR

This paper introduces a novel, efficient method for sampling conditioned Markov jump processes by leveraging Gaussian approximations, improving computational efficiency in simulation-based inference.

Contribution

The paper presents a new, computationally efficient approach for approximating conditioned hazards in MJPs using Gaussian approximations, enhancing existing sampling methods.

Findings

The proposed method is faster than existing approaches.

It provides accurate approximations of conditioned MJPs.

Validated through three illustrative examples.

Abstract

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.