Markov jump processes (MJPs) are continuous-time stochastic processes widely used in a variety of applied disciplines. Inference for MJPs typically proceeds via Markov chain Monte Carlo, the state-of-the-art being a uniformization-based auxiliary variable Gibbs sampler. This was designed for situations where the MJP parameters are known, and Bayesian inference over unknown parameters is typically carried out by incorporating it into a larger Gibbs sampler. This strategy of sampling parameters given path, and path given parameters can result in poor Markov chain mixing. In this work, we propose a simple and elegant algorithm to address this problem. Our scheme brings Metropolis-Hastings approaches for discrete-time hidden Markov models to the continuous-time setting, resulting in a complete and clean recipe for parameter and path inference in MJPs. In our experiments, we demonstrate superior performance over Gibbs sampling, as well as another popular approach, particle MCMC. We also show our sampler inherits geometric mixing from an `ideal' sampler that operates without computational constraints.

中文翻译：

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马尔可夫跳跃过程的有效参数采样

马尔可夫跳跃过程 (MJP) 是广泛用于各种应用学科的连续时间随机过程。MJP 的推理通常通过马尔可夫链蒙特卡罗进行，最先进的技术是基于统一化的辅助变量 Gibbs 采样器。这是为 MJP 参数已知的情况而设计的，对未知参数的贝叶斯推断通常是通过将其合并到更大的 Gibbs 采样器中来执行的。这种采样参数给定路径和路径给定参数的策略会导致马尔可夫链混合不佳。在这项工作中，我们提出了一个简单而优雅的算法来解决这个问题。我们的方案将离散时间隐马尔可夫模型的 Metropolis-Hastings 方法引入到连续时间设置中，从而为 MJP 中的参数和路径推断提供了完整而清晰的方法。在我们的实验中，我们展示了优于 Gibbs 采样的性能，以及另一种流行的方法，粒子 MCMC。我们还展示了我们的采样器继承了“理想”采样器的几何混合，该采样器在没有计算约束的情况下运行。