Mathematics – Numerical Analysis
Scientific paper
2011-09-13
Mathematics
Numerical Analysis
17 pages. 2 Figures, 3 tables
Scientific paper
We present an efficient finite difference method for the computation of parameter sensitivities for a wide class of continuous time Markov chains. The motivating class of models, and the source of our examples, are the stochastic chemical kinetic models commonly used in the biosciences, though other natural application areas include population processes and queuing networks. The method is essentially derived by making effective use of the random time change representation of Kurtz, and is no harder to implement than any standard continuous time Markov chain algorithm, such as "Gillespie's algorithm" or the next reaction method. Further, the method is analytically tractable, and, for a given number of realizations of the stochastic process, produces an estimator with substantially lower variance than that obtained using other common methods. Therefore, the computational complexity required to solve a given problem is lowered greatly. In this work, we present the method together with the theoretical analysis detailing the variance of the resulting estimator of the sensitivities. We also provide numerical examples comparing the method developed here to other common methods.
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