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Efficient sampling of conditioned Markov jump processes

机译：有效采样条件马尔可夫跳跃过程

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摘要

We consider the task of generating draws from a Markov jump process (MJP) between two time points at which the process is known. Resulting draws are typically termed bridges, and the generation of such bridges plays a key role in simulation-based inference algorithms for MJPs. The problem is challenging due to the intractability of the conditioned process, necessitating the use of computationally intensive methods such as weighted resampling or Markov chain Monte Carlo. An efficient implementation of such schemes requires an approximation of the intractable conditioned hazard/propensity function that is both cheap and accurate. In this paper, we review some existing approaches to this problem before outlining our novel contribution. Essentially, we leverage the tractability of a Gaussian approximation of the MJP and suggest a computationally efficient implementation of the resulting conditioned hazard approximation. We compare and contrast our approach with existing methods using three examples.
机译：我们考虑从已知过程的两个时间点之间的Markov跳跃过程（MJP）生成抽奖的任务。产生的抽奖通常称为“桥梁”，这种桥梁的生成在MJP的基于仿真的推理算法中起着关键作用。由于条件处理的难处理性，该问题具有挑战性，需要使用计算密集型方法，例如加权重采样或马尔可夫链蒙特卡洛。这种方案的有效实施需要廉价且准确的近似难处理条件危险/倾向函数。在本文中，我们在概述我们的新贡献之前回顾了一些解决该问题的现有方法。本质上，我们利用MJP的高斯近似的易处理性，并建议在计算上有效地实现所得条件危害近似。我们使用三个示例将我们的方法与现有方法进行比较和对比。

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