Unbiased Bayesian Inference for Population Markov Jump Processes via Random Truncations

TL;DR

This paper introduces a novel pseudo-marginal sampling algorithm using random truncations for Bayesian inference in population Markov Jump processes, enabling efficient and accurate analysis of infinite state-space systems.

Contribution

The paper presents a new algorithm that efficiently performs joint state and parameter inference in continuous-time Markov processes with infinite states using random truncation techniques.

Findings

Achieves significant computational savings over existing methods.

Maintains high accuracy and fast convergence.

Demonstrates practical applicability with synthetic biology data.

Abstract

We consider continuous time Markovian processes where populations of individual agents interact stochastically according to kinetic rules. Despite the increasing prominence of such models in fields ranging from biology to smart cities, Bayesian inference for such systems remains challenging, as these are continuous time, discrete state systems with potentially infinite state-space. Here we propose a novel efficient algorithm for joint state / parameter posterior sampling in population Markov Jump processes. We introduce a class of pseudo-marginal sampling algorithms based on a random truncation method which enables a principled treatment of infinite state spaces. Extensive evaluation on a number of benchmark models shows that this approach achieves considerable savings compared to state of the art methods, retaining accuracy and fast convergence. We also present results on a synthetic biology data set showing the potential for practical usefulness of our work.