标题： 离散观测的连续时间马尔可夫链的有效贝叶斯推断 显示英文标题

标题： Efficient Bayesian Inference for Discretely Observed Continuous Time Markov Chains

摘要： 连续时间马尔可夫链（CTMC）的推断在过程仅在离散时间点被观测时变得具有挑战性。 精确似然难以处理，现有的方法即使在中等维度的状态空间中也常常遇到困难。 我们提出了一种基于伪似然的可扩展贝叶斯框架，以绕过对完整难以处理的似然的需求。 我们的方法联合估计概率转移矩阵和生成器的双正交谱分解，从而实现一个符合嵌入性的高效吉布斯采样过程。 现有方法通常会积分掉未观测到的转移，这在数据量或维度增加时会变得计算负担沉重。 我们方法的计算成本在数据数量上几乎不变，并且可以很好地扩展到中高维度。 我们通过建立理论保证来证明我们的伪似然方法，包括概率转移矩阵的伯恩斯坦-冯·米塞斯定理以及生成器谱参数的后验一致性。 通过模拟和应用，我们展示了我们方法的灵活性和鲁棒性，为CTMC的贝叶斯推断提供了一种可行且可扩展的方法。 显示英文摘要

摘要： Inference for continuous-time Markov chains (CTMCs) becomes challenging when the process is only observed at discrete time points. The exact likelihood is intractable, and existing methods often struggle even in medium-dimensional state-spaces. We propose a scalable Bayesian framework for CTMC inference based on a pseudo-likelihood that bypasses the need for the full intractable likelihood. Our approach jointly estimates the probability transition matrix and a biorthogonal spectral decomposition of the generator, enabling an efficient Gibbs sampling procedure that obeys embeddability. Existing methods typically integrate out the unobserved transitions, which becomes computationally burdensome as the number of data or dimensions increase. The computational cost of our method is near-invariant in the number of data and scales well to medium-high dimensions. We justify our pseudo-likelihood approach by establishing theoretical guarantees, including a Bernstein-von Mises theorem for the probability transition matrix and posterior consistency for the spectral parameters of the generator. Through simulation and applications, we showcase the flexibility and robustness of our approach, offering a tractable and scalable approach to Bayesian inference for CTMCs.