Stochastic Filtering of Reaction Networks Partially Observed in Time Snapshots

TL;DR

This paper introduces a particle filtering method for estimating the conditional distribution of stochastic reaction networks observed at discrete time points, leveraging linear constraints and Poisson proposals for improved accuracy.

Contribution

The paper presents a novel targeting particle filtering approach that accounts for linear constraints and uses inhomogeneous Poisson proposals, enhancing estimation in partially observed reaction networks.

Findings

The method accurately estimates conditional distributions in reaction networks.

Numerical examples demonstrate improved performance over existing methods.

The approach effectively incorporates linear constraints between observations.

Abstract

Stochastic reaction network models arise in intracellular chemical reactions, epidemiological models and other population process models, and are a class of continuous time Markov chains which have the nonnegative integer lattice as state space. We consider the problem of estimating the conditional probability distribution of a stochastic reaction network given exact partial state observations in time snapshots. We propose a particle filtering method called the targeting method. Our approach takes into account that the reaction counts in between two observation snapshots satisfy linear constraints and also uses inhomogeneous Poisson processes as proposals for the reaction counts to facilitate exact interpolation. We provide rigorous analysis as well as numerical examples to illustrate our method and compare it with other alternatives.