  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.
