Coupling sample paths to the partial thermodynamic limit in stochastic chemical reaction networks

TL;DR

This paper investigates coupling exact stochastic process paths with their thermodynamic limit to reduce variance and computational cost in Monte Carlo simulations of biochemical systems.

Contribution

It introduces a coupling method between exact and approximate models to improve efficiency and provides rigorous analysis and numerical validation of computational gains.

Findings

Coupling reduces variance in Monte Carlo estimators.

Numerical simulations confirm significant computational savings.

Theoretical analysis supports asymptotic efficiency improvements.

Abstract

Many biochemical systems appearing in applications have a multiscale structure so that they converge to piecewise deterministic Markov processes in a thermodynamic limit. The statistics of the piecewise deterministic process can be obtained much more efficiently than those of the exact process. We explore the possibility of coupling sample paths of the exact model to the piecewise deterministic process in order to reduce the variance of their difference. We then apply this coupling to reduce the computational complexity of a Monte Carlo estimator. In addition to rigorous results concerning the asymptotic computational complexity of the Monte Carlo estimator, numerical simulations are performed on some simple biological models confirming that computational gains are made.