  Estimation of parameter sensitivities for stochastic chemical reaction
networks is an important and challenging problem. Sensitivity values are
important in the analysis, modeling and design of chemical networks. They help
in understanding the robustness properties of the system and also in
identifying the key reactions for a given outcome. In a discrete setting, most
of the methods that exist in the literature for the estimation of parameter
sensitivities rely on Monte Carlo simulations along with finite difference
computations. However these methods introduce a bias in the sensitivity
estimate and in most cases the size or direction of the bias remains unknown,
potentially damaging the accuracy of the analysis. In this paper, we use the
random time change representation of Kurtz to derive an exact formula for
parameter sensitivity. This formula allows us to construct an unbiased
estimator for parameter sensitivity, which can be efficiently evaluated using a
suitably devised Monte Carlo scheme. The existing literature contains only one
method to produce such an unbiased estimator. This method was proposed by
Plyasunov and Arkin and it is based on the Girsanov measure transformation. By
taking a couple of examples we compare our method to this existing method. Our
results indicate that our method can be much faster than the existing method
while computing sensitivity with respect to a reaction rate constant which is
small in magnitude. This rate constant could correspond to a reaction which is
slow in the reference time-scale of the system. Since many biological systems
have such slow reactions, our method can be a useful tool for sensitivity
analysis.
