State and parameter estimation from exact partial state observation in stochastic reaction networks

TL;DR

This paper introduces a novel particle filter method for exact state and parameter estimation in stochastic reaction networks, leveraging continuous-time observations of some species to improve inference accuracy.

Contribution

It presents a new particle filtering approach that models the conditional distribution of unobserved states via differential equations with jumps, enabling efficient Bayesian parameter and past state estimation.

Findings

Effective simulation of unobserved species states with weights

Accurate Bayesian parameter estimation from partial observations

Applicable to past state estimation using future observations

Abstract

We consider chemical reaction networks modeled by a discrete state and continuous in time Markov process for the vector copy number of the species and provide a novel particle filter method for state and parameter estimation based on exact observation of some of the species in continuous time. The conditional probability distribution of the unobserved states is shown to satisfy a system of differential equations with jumps. We provide a method of simulating a process that is a proxy for the vector copy number of the unobserved species along with a weight. The resulting weighted Monte Carlo simulation is then used to compute the conditional probability distribution of the unobserved species. We also show how our algorithm can be adapted for a Bayesian estimation of parameters and for the estimation of a past state value based on observations up to a future time.