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

Abstract

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.

Parameter estimation in stochastic chemical kinetic models using derivative free optimization and bootstrapping

“…We are evaluating the effectiveness of derivatives estimates obtained by a good sensitivity estimator, e.g. coupled-finite difference [1, 47], in performing the parameter estimation in stochastic chemical kinetic models.…”

Hybrid pathwise sensitivity methods for discrete stochastic models of chemical reaction systems

“…Due to the importance of having reliable numerical estimators for gradients, there has recently been a plethora of research articles focusing on their development and analysis [2,5,18,20,24,26,28,30,31]. There are three main classes of methods that carry out the task of estimating these derivatives: finite difference methods, likelihood ratio methods, and pathwise methods.…”

Efficient estimators for likelihood ratio sensitivity indices of complex stochastic dynamics

“…In this paper we compare the estimatorĪ 3 to the standard LR estimators I 2 andĪ 2 [11], as well as the coupled finite difference method I 1 [1] and I 5 in order to have a benchmark comparison with a highly efficient, low variance method [23,22]. We also consider the truncated LRĪ 4 which-likeĪ 3 -provides a gradient-free, low variance method for sensitivity analysis at stationarity, although it relies on the accurate calculation of decorrelation times T d = T d (f ) in (10) for all observables f of interest.…”

“…standard normal random variables. The process X n is a discrete time Markov chain with a continuous state space and using the transition probabilities of X n one finds, as in (23), that W θ (X 0:T ) = N n=1 Γ(X n−1 ) √ ∆t ∆B n ,…”