Rate estimation in partially observed Markov jump processes with measurement errors

TL;DR

This paper introduces a simulation-based Bayesian approach for estimating rates in Markov jump processes with measurement errors, avoiding diffusion approximations and handling missing data effectively.

Contribution

It develops novel MCMC and particle filter algorithms for Bayesian rate estimation in partially observed Markov jump processes without relying on diffusion approximations.

Findings

Effective in data-poor scenarios

Applied to biological and chemical models

Accurate posterior sampling of rates

Abstract

We present a simulation methodology for Bayesian estimation of rate parameters in Markov jump processes arising for example in stochastic kinetic models. To handle the problem of missing components and measurement errors in observed data, we embed the Markov jump process into the framework of a general state space model. We do not use diffusion approximations. Markov chain Monte Carlo and particle filter type algorithms are introduced, which allow sampling from the posterior distribution of the rate parameters and the Markov jump process also in data-poor scenarios. The algorithms are illustrated by applying them to rate estimation in a model for prokaryotic auto-regulation and in the stochastic Oregonator, respectively.