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Bayesian inference for continuous-time hidden Markov models with an unknown number of states

机译：贝叶斯人推断连续时间隐马尔可夫模型，州数量未知

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摘要

We consider the modeling of data generated by a latent continuous-time Markov jump process with a state space of finite but unknown dimensions. Typically in such models, the number of states has to be pre-specified, and Bayesian inference for a fixed number of states has not been studied until recently. In addition, although approaches to address the problem for discrete-time models have been developed, no method has been successfully implemented for the continuous-time case. We focus on reversible jump Markov chain Monte Carlo which allows the trans-dimensional move among different numbers of states in order to perform Bayesian inference for the unknown number of states. Specifically, we propose an efficient split-combine move which can facilitate the exploration of the parameter space, and demonstrate that it can be implemented effectively at scale. Subsequently, we extend this algorithm to the context of model-based clustering, allowing numbers of states and clusters both determined during the analysis. The model formulation, inference methodology, and associated algorithm are illustrated by simulation studies. Finally, we apply this method to real data from a Canadian healthcare system in Quebec.
机译：我们考虑通过有限但未知维度的状态空间模拟由潜在连续时间马尔可夫跳跃过程产生的数据的建模。通常在这种模型中，必须预先指定状态的数量，并且在最近尚未研究固定数量状态的贝叶斯推理。此外，虽然已经开发出解决离散时间模型问题的方法，但是没有成功实现了连续时间案例的方法。我们专注于可逆跳跃马尔可夫链蒙特卡罗，它允许不同数量的状态之间的跨维移动，以便对未知数量的州进行贝叶斯人推断。具体地，我们提出了一种有效的分离组合，可以促进参数空间的探索，并证明它可以在规模上有效地实现。随后，我们将该算法扩展到基于模型的群集的上下文，允许在分析期间确定的状态和群集。模型配方，推理方法和相关算法通过仿真研究说明。最后，我们将这种方法应用于魁北克的加拿大医疗保健系统的实际数据。

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