Steady-state sensitivity analysis of continuous time Markov chains

Ting Wang, Petr Plechac

Abstract: In this paper we study Monte Carlo estimators based on the likelihood ratio approach for steady-state sensitivity. We first extend the result of Glynn and Olvera-Cravioto [Stoch. Syst., to appear] to the setting of continuous time Markov chains with a countable state space which include models such as stochastic reaction kinetics and kinetic Monte Carlo lattice systems. We show that the variance of the centered likelihood ratio estimators does not grow in time. This result suggests that the centered likelihood ratio estimators should be favored for sensitivity analysis when the mixing time of the underlying continuous time Markov chain is large, which is typically the case when systems exhibit multiscale behavior. We demonstrate a practical implication of this analysis with two numerical benchmarks of biochemical reaction networks.