MCMC inference for Markov Jump Processes via the Linear Noise Approximation

TL;DR

This paper introduces a Riemann manifold MCMC approach for Bayesian inference in Markov jump processes, leveraging a likelihood approximation valid near the thermodynamic limit to enable efficient and fast inference in complex systems.

Contribution

It presents a novel application of Riemann manifold MCMC with a likelihood approximation for Markov jump processes, improving computational efficiency and convergence.

Findings

Efficient Bayesian inference achieved for complex Markov jump processes.

The method demonstrates fast mixing and convergence in chemical kinetics and systems biology examples.

Approximate likelihood approach is effective near the thermodynamic limit.

Abstract

Bayesian analysis for Markov jump processes is a non-trivial and challenging problem. Although exact inference is theoretically possible, it is computationally demanding thus its applicability is limited to a small class of problems. In this paper we describe the application of Riemann manifold MCMC methods using an approximation to the likelihood of the Markov jump process which is valid when the system modelled is near its thermodynamic limit. The proposed approach is both statistically and computationally efficient while the convergence rate and mixing of the chains allows for fast MCMC inference. The methodology is evaluated using numerical simulations on two problems from chemical kinetics and one from systems biology.