A finite difference method for estimating second order parameter sensitivities of discrete stochastic chemical reaction networks

TL;DR

This paper introduces an efficient finite difference approach for estimating second derivatives of expectations in stochastic chemical networks, significantly reducing variance and computational effort, with potential applications in optimization and Markov chain modeling.

Contribution

The paper proposes a novel coupling-based finite difference method that lowers variance and computational cost for second derivative estimation in stochastic systems.

Findings

Reduces variance compared to existing methods

Lower computational complexity demonstrated

Applicable to continuous time Markov chains

Abstract

We present an efficient finite difference method for the approximation of second derivatives, with respect to system parameters, of expectations for a class of discrete stochastic chemical reaction networks. The method uses a coupling of the perturbed processes that yields a much lower variance than existing methods, thereby drastically lowering the computational complexity required to solve a given problem. Further, the method is simple to implement and will also prove useful in any setting in which continuous time Markov chains are used to model dynamics, such as population processes. We expect the new method to be useful in the context of optimization algorithms that require knowledge of the Hessian.