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.
翻译:我们为贝叶斯人就离散观测的连续时间马尔科夫跳跃过程的速率参数提出新的推论方法,这种连续观测的马尔科夫跳跃过程具有可计算到无限的状态空间。通常的推论方法,即微粒马尔科夫链蒙特卡洛(Particle MCMC),当观测噪音很小时挣扎。我们考虑了最具有挑战性的精确观测机制,并提供了两种新的推论方法:最小的扩展国家空间算法(MESA)和国家空间算法(nMESA),通过扩展马尔科夫链蒙特卡洛州空间,蒙卡洛州和尼奥萨州均使用定速矩阵的推推法,对马尔科夫跳动过程进行精确的贝斯语推论,尽管其空间是可计算到无限的。 数字实验显示,微粒MC在三至几级的大小要素之间有所改进。