Parametric Sensitivity Analysis of Stochastic Reaction Networks

Abstract

Reaction networks are systems consisting of several species interacting with each other through a set of predefined reaction channels. Models of real world reaction systems often contain several parameters which play a significant role in determining the system's dynamics. Therefore, parametric sensitivity analysis is an essential tool for the modeling and parameter estimation process. Due to the complex and random nature of the reaction systems, among all approaches for sensitivity analysis, Monte Carlo simulation is the most suitable for the parametric sensitivity analysis because its complexity does not grow dramatically as the problem dimension grows. Most Monte Carlo methods for sensitivity analysis can be classified into three categories, the pathwise derivative (PD), the finite difference (FD) and the Girsanov transformation (GT). Comparisons of these methods for specific examples have been done by many researchers, which showed that when applicable, the PD method and FD method tend to outperform the GT method. However, to the best of our knowledge, no existing literature studies these observations from a theoretical point of view. In this thesis, we provide a theoretical justification for these observations in terms of system size asymptotic analysis. We also examine our result by testing several numerical examples. Other than the analysis for the efficiency of these Monte Carlo estimators, we also provide some sufficient conditions which guarantee the validity of the GT method. Finally, for an ergodic system, there exists a steady state distribution and hence it is reasonable for us to consider the steady state sensitivity estimation problem. We establish an asymptotic correlation result and use this result to justify the ensemble-averaged correlation function method introduced in the literature.