Comparison of finite difference based methods to obtain sensitivities of stochastic chemical kinetic models

Sensitivity analysis is a powerful tool in determining parameters to which the system output is most responsive, in assessing robustness of the system to extreme circumstances or unusual environmental conditions, in identifying rate limiting pathways as a candidate for drug delivery, and in parameter estimation for calculating the Hessian of the objective function. Anderson [SIAM J. Numer. Anal. 50, 2237 (2012)] shows the advantages of the newly developed coupled finite difference (CFD) estimator over the common reaction path (CRP) [M. Rathinam, P. W. Sheppard, and M. Khammash, J. Chem. Phys. 132, 034103 (2010)] estimator. In this paper, we demonstrate the superiority of the CFD estimator over the common random number (CRN) estimator in a number of scenarios not considered previously in the literature, including the sensitivity of a negative log likelihood function for parameter estimation, the sensitivity of being in a rare state, and a sensitivity with fast fluctuating species. In all examples considered, the superiority of CFD over CRN is demonstrated. We also provide an example in which the CRN method is superior to the CRP method, something not previously observed in the literature. These examples, along with Anderson's results, lead to the conclusion that CFD is currently the best estimator in the class of finite difference estimators of stochastic chemical kinetic models.