Multilevel Splitting for Reachability Analysis of Stochastic Hybrid Systems

Biochemical research is increasingly using formal modeling, simulation, and analysis methods to improve the understanding of complex systems. Probabilistic analysis techniques such as Monte Carlo methods can be used to determine reachability or safety probabilities for large Stochastic Hybrid System (SHS) models, but systems containing influential rare events may require prohibitively large numbers of realizations to generate accurate estimates. In this work we present a multilevel splitting variance reduction method for SHS that improves the accuracy and efficiency of Monte Carlo methods for rare events. We apply the approach for reachability analysis of a SHS model of glycolysis, which is a biochemical energy conversion process found in virtually every living cell. We also present a method for selecting the variance reduction parameters as well as accuracy and efficiency analysis of our techniques.