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

摘要

We present an efficient finite difference method for the approximation ofsecond derivatives, with respect to system parameters, of expectations for aclass of discrete stochastic chemical reaction networks. The method uses acoupling of the perturbed processes that yields a much lower variance thanexisting methods, thereby drastically lowering the computational complexityrequired to solve a given problem. Further, the method is simple to implementand will also prove useful in any setting in which continuous time Markovchains are used to model dynamics, such as population processes. We expect thenew method to be useful in the context of optimization algorithms that requireknowledge of the Hessian.