We consider continuous time Markovian processes where populations of individual agents interact stochastically according to kinetic rules. Despite the increasing prominence of such models in fields ranging from biology to smart cities, Bayesian inference for such systems remains challenging, as these are continuous time, discrete state systems with potentially infinite state-space. Here we propose a novel efficient algorithm for joint state/parameter posterior sampling in population Markov Jump processes. We introduce a class of pseudo-marginal sampling algorithms based on a random truncation method which enables a principled treatment of infinite state spaces. Extensive evaluation on a number of benchmark models shows that this approach achieves considerable savings compared to state of the art methods, retaining accuracy and fast convergence. We also present results on a synthetic biology data set showing the potential for practical usefulness of our work.

中文翻译：

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通过随机截断对种群马尔可夫跳跃过程进行无偏贝叶斯推断。

我们考虑连续时间的马尔可夫过程，其中各个个体的种群根据动力学规则随机地相互作用。尽管此类模型在从生物学到智能城市的各个领域中越来越重要，但贝叶斯对此类系统的推理仍然具有挑战性，因为它们是连续时间，具有潜在无限状态空间的离散状态系统。在这里，我们提出了一种新的有效算法，用于种群马尔可夫跳跃过程中的联合状态/参数后验采样。我们介绍了一种基于随机截断方法的伪边际采样算法，该算法可以对无限状态空间进行原则性处理。对许多基准模型的广泛评估表明，与最先进的方法相比，该方法可节省大量成本，并保持准确性和快速收敛性。