论文标题
在终端约束下对马尔可夫跳跃过程的分析
Analysis of Markov Jump Processes under Terminal Constraints
论文作者
论文摘要
许多概率的推理问题，例如随机过滤或稀有事件概率的计算，都需要在初始和终端约束下进行模型分析。我们为广泛使用的种群结构的马尔可夫跳跃过程提供了解决这个桥接问题的解决方案。该方法基于一个状态空间集结方案，该方案在网格结构中汇总状态。所得的近似桥接分布用于迭代地完善状态空间的相关和截断。这样，该算法就可以在端点约束下学习一个完善的有限状态投影，可为系统行为提供保证的下限。我们证明了该方法适用于贝叶斯推论等多种问题的适用性和对罕见事件的分析。
Many probabilistic inference problems such as stochastic filtering or the computation of rare event probabilities require model analysis under initial and terminal constraints. We propose a solution to this bridging problem for the widely used class of population-structured Markov jump processes. The method is based on a state-space lumping scheme that aggregates states in a grid structure. The resulting approximate bridging distribution is used to iteratively refine relevant and truncate irrelevant parts of the state-space. This way the algorithm learns a well-justified finite-state projection yielding guaranteed lower bounds for the system behavior under endpoint constraints. We demonstrate the method's applicability to a wide range of problems such as Bayesian inference and the analysis of rare events.
