Splitting for Rare Event Simulation in Biochemical Systems

Estimating the probability of rare events in biochemical systems is an important task, since it can help in studying rare abnormal behavior when they do occur. A conventional Monte Carlo approach for such a task would be to simulate a system through a standard stochastic simulation algorithm (SSA), hence generating many trajectories and counting the number of the successful ones. Rare events make this approach infeasible since a prohibitively large number of trajectories would need to be generated before the estimation becomes reasonably accurate.

In this paper we propose a new method, called sSSA, which estimates the probability for a rare event through a kind of biased simulation. The state space is split into interfaces defined through corresponding levels, and simulated trajectories are gradually ``pushed'' towards the rare event following such levels. The (unbiased) probability for the rare event is then estimated by counting the successful (biased) trajectories, and then applying a correction factor so to account for the bias.

We compare both performance and accuracy for SSA and sSSA by experimenting in some concrete scenarios. Experimental results prevail that sSSA is more efficient than the naive SSA approach.