We consider the problem of computing first-passage time distributions for reaction processes modeled 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 trimerization process and show good agreement with stochastic simulations.

中文翻译：

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首次通过时间分布的低阶有效逼近

我们考虑了对由主方程建模的反应过程计算首次通过时间分布的问题。我们证明，这一类普遍棘手的问题等同于辅助观察过程的顺序贝叶斯推理问题。通过求解一组封闭的耦合常微分方程（对于过程的低阶矩）（该过程的低阶矩），其大小随物种数量而定，可以有效地近似求解该问题。我们将其应用于流行病模型和三聚化过程，并显示出与随机模拟的良好一致性。