Unbiased estimation of second-order parameter sensitivities for stochastic reaction networks

TL;DR

This paper presents an unbiased, easy-to-implement estimator for second-order parameter sensitivities in stochastic reaction networks, extending previous first-order sensitivity methods and enabling more accurate optimization techniques.

Contribution

It introduces an exact representation for second-order sensitivities and constructs an unbiased estimator using coupling methods, advancing sensitivity analysis in stochastic networks.

Findings

Provides an unbiased estimator for second-order sensitivities.

Extends coupling techniques from first-order to second-order sensitivities.

Facilitates more accurate optimization in stochastic reaction networks.

Abstract

This paper deals with the problem of estimating second-order parameter sensitivities for stochastic reaction networks, where the reaction dynamics is modeled as a continuous time Markov chain over a discrete state space. Estimation of such second-order sensitivities (the Hessian) is necessary for implementing the Newton-Raphson scheme for optimization over the parameter space. To perform this estimation, Wolf and Anderson have proposed an efficient finite-difference method, that uses a coupling of perturbed processes to reduce the estimator variance. The aim of this paper is to illustrate that the same coupling can be exploited to derive an exact representation for second-order parameter sensitivity. Furthermore with this representation one can construct an unbiased estimator which is easy to implement. The ideas contained in this paper are extensions of the ideas presented in our recent papers on first-order parameter sensitivity estimation.