Efficient Low-Order Approximation of First-Passage Time Distributions

Microsoft Research, Cambridge, UK We consider the problem of computing first-passage time distributions for reaction processes modelled by master equations. We show that this generally intractable class of problems is equivalent to a sequential Bayesian inference problem for an auxiliary observation process. The solution can be approximated efficiently by solving a closed set of coupled ordinary differential equations (for the low-order moments of the process) whose size scales with the number of species. We apply it to an epidemic model and a trimerisation process, and show good agreement with stochastic simulations. Many systems in nature consist of stochastically interacting agents or particles. Such systems are frequently modelled as reaction processes whose dynamics are described by master equations [1].