论文标题
贝叶斯推断，用于离散观察到的连续时间多状态模型
Bayesian inference for discretely observed continuous time multi-state models
论文作者
论文摘要
多状态模型经常用于表示通过一组离散状态发展的过程。当状态之间的过渡可能取决于进入当前状态的时间或从过程开始时经过的时间时，多状态模型的重要类别会产生。前者被称为半马尔可夫，而后者被称为不均匀的马尔可夫模型。当仅在离散时间点观察到该过程时，两种模型的推断都列出了计算困难，而没有有关状态过渡的其他信息。实际上，在这两种情况下，可能性函数都无法以封闭形式获得。为了在这两类模型下获得贝叶斯的推断，我们通过大都会危机算法在观测点上重建整个未观察到的轨迹。作为提议密度，我们使用的是嵌套的马尔可夫模型给出的，其条件轨迹可以通过均匀化技术轻松绘制。通过仿真研究和对多状态模型的两个基准数据集进行了分析来说明所得的推论。
Multi-state models are frequently applied for representing processes evolving through a discrete set of state. Important classes of multi-state models arise when transitions between states may depend on the time since entry into the current state or on the time elapsed from the starting of the process. The former models are called semi-Markov while the latter are known as inhomogeneous Markov models. Inference for both the models presents computational difficulties when the process is only observed at discrete time points with no additional information about the state transitions. Indeed, in both the cases, the likelihood function is not available in closed form. In order to obtain Bayesian inference under these two classes of models we reconstruct the whole unobserved trajectories conditioned on the observed points via a Metropolis-Hastings algorithm. As proposal density we use that given by the nested Markov models whose conditioned trajectories can be easily drawn by the uniformization technique. The resulting inference is illustrated via simulation studies and the analysis of two benchmark data sets for multi state models.
