Stochastic reaction network models arise in intracellular chemical reactions, epidemiological models and other population process models, and are a class of continuous time Markov chains which have the nonnegative integer lattice as state space. We consider the problem of estimating the conditional probability distribution of a stochastic reaction network given exact partial state observations in time snapshots. We propose a particle filtering method called the targeting method. Our approach takes into account that the reaction counts in between two observation snapshots satisfy linear constraints and also uses inhomogeneous Poisson processes as proposals for the reaction counts to facilitate exact interpolation. We provide rigorous analysis as well as numerical examples to illustrate our method and compare it with other alternatives.

翻译：随机反应网络模型源于细胞内化学反应、流行病模型及其他种群过程模型，这是一类以非负整数格为状态空间的连续时间马尔可夫链。我们考虑在时间快照中给定精确的部分状态观测值下，估计随机反应网络条件概率分布的问题。提出一种称为靶向方法的粒子滤波方法。我们的方法利用了两次观测快照之间的反应计数满足线性约束这一特性，并采用非齐次泊松过程作为反应计数的建议分布以实现精确插值。我们通过严格的理论分析和数值算例展示了该方法的效果，并与其他替代方案进行了比较。