Solving stochastic chemical kinetics by Metropolis Hastings sampling

TL;DR

This paper introduces a Metropolis-Hastings sampling method using SSA and CME-based solvers to efficiently simulate stochastic chemical reactions, ensuring samples match the SSA distribution.

Contribution

It presents a novel Metropolis-Hastings approach leveraging CME-based solvers to improve stochastic chemical kinetics simulation accuracy and efficiency.

Findings

Samples match SSA distribution

Histogram convergence demonstrated

Method accelerates tau-leap accuracy

Abstract

This study considers using Metropolis-Hastings algorithm for stochastic simulation of chemical reactions. The proposed method uses SSA (Stochastic Simulation Algorithm) distribution which is a standard method for solving well-stirred chemically reacting systems as a desired distribution. A new numerical solvers based on exponential form of exact and approximate solutions of CME (Chemical Master Equation) is employed for obtaining target and proposal distributions in Metropolis-Hastings algorithm to accelerate the accuracy of the tau-leap method. Samples generated by this technique have the same distribution as SSA and the histogram of samples show it's convergence to SSA.