论文标题
确切的贝叶斯推断，用于使用有限速率矩阵的离散观察到的马尔可夫跳跃过程
Exact Bayesian inference for discretely observed Markov Jump Processes using finite rate matrices
论文作者
论文摘要
我们提出了贝叶斯推断的新方法，以离散观察到的连续时间马尔可夫跳跃过程具有无限状态空间的速率参数。粒子马尔可夫链蒙特卡洛（粒子MCMC）的通常选择方法，当观察噪声很小时会挣扎。我们考虑了最具挑战性的确切观察方案，并在这种情况下提供了两种新方法：最小的扩展状态空间算法（MESA）和几乎最小的扩展状态空间算法（NMESA）。通过扩展Markov链蒙特卡洛州空间，MESA和NMESA都使用有限速率矩阵的启用来对马尔可夫跳跃过程进行精确的贝叶斯推断，即使其状态空间是无数的。数值实验表明，粒子MCMC的改进在三个和几个数量级之间。
We present new methodologies for Bayesian inference on the rate parameters of a discretely observed continuous-time Markov jump processes with a countably infinite state space. 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 state space algorithm (MESA) and the nearly minimal extended state space algorithm (nMESA). By extending the Markov chain Monte Carlo state space, both MESA and nMESA use the exponentiation of finite rate matrices to perform exact Bayesian inference on the Markov jump process even though its state space is countably infinite. Numerical experiments show improvements over particle MCMC of between a factor of three and several orders of magnitude.
