Efficient Low-Order Approximation of First-Passage Time Distributions
This provides an efficient method for researchers in computational biology and chemistry to approximate first-passage times in complex reaction processes, though it is incremental as it builds on existing master equation frameworks.
The paper tackled the problem of computing first-passage time distributions for reaction processes, which is generally intractable, by showing equivalence to a sequential Bayesian inference problem and approximating it efficiently with coupled ODEs that scale with species number, achieving good agreement with stochastic simulations in epidemic and trimerisation models.
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.