ABSTRACT

We present new methodologies for Bayesian inference on the rate parameters of a discretely observed continuous-time Markov jump process with a countably infinite statespace. The usual method of choice for inference, particle Markov chain Monte Carlo (particle MCMC), struggles when the observation noise is small. We consider the most challenging regime of exact observations and provide two new methodologies for inference in this case: the minimal extended statespace algorithm (MESA) and the nearly minimal extended statespace algorithm (nMESA). By extending the Markov chain Monte Carlo statespace, both MESA and nMESA use the exponentiation of finite rate matrices to perform exact Bayesian inference on the Markov jump process even though its statespace is countably infinite. Numerical experiments show improvements over particle MCMC of between a factor of three and several orders of magnitude. Supplementary materials for this article are available online.

摘要

我们提出了新的贝叶斯推理方法，用于对具有可数无限状态空间的离散观察到的连续时间马尔可夫跳跃过程的速率参数进行推断。通常选择的推理方法，粒子马尔可夫链蒙特卡罗（粒子 MCMC），在观察噪声较小时会遇到困难。我们考虑了最具挑战性的精确观察机制，并在这种情况下提供了两种新的推理方法：最小扩展状态空间算法 (MESA) 和近最小扩展状态空间算法 (nMESA)。通过扩展马尔可夫链蒙特卡洛状态空间，MESA 和 nMESA 都使用有限速率矩阵的幂来对马尔可夫跳跃过程执行精确贝叶斯推理，即使其状态空间是可数无限的。数值实验表明，粒子 MCMC 的改进幅度在三个到几个数量级之间。本文的补充材料可在线获取。