论文标题
估计马尔可夫跳跃过程的吸收时间分布
Estimating absorption time distributions of general Markov jump processes
论文作者
论文摘要
马尔可夫跳跃过程的吸收时间分布的估计是统计和应用概率的各个分支中的重要任务。尽管时间均匀的情况是经典的，但由于其增加的灵活性和计算能力的进步，该时间均匀的情况最近受到了越来越多的关注。但是，假定通勤的亚强度矩阵，在各种情况下，这限制了所得表示的简约特性。本文开发了通过最大似然估计，尤其是使用期望最大化算法来解决一般情况所需的理论。提出了对分段恒定强度矩阵函数的减少，以提供简洁的表示，其中参数线性模型将强度结合在一起。从矩阵分析方法的角度来看，通过众所周知的要求理论分布和真实数据来讨论和说明实际方面。
The estimation of absorption time distributions of Markov jump processes is an important task in various branches of statistics and applied probability. While the time-homogeneous case is classic, the time-inhomogeneous case has recently received increased attention due to its added flexibility and advances in computational power. However, commuting sub-intensity matrices are assumed, which in various cases limits the parsimonious properties of the resulting representation. This paper develops the theory required to solve the general case through maximum likelihood estimation, and in particular, using the expectation-maximization algorithm. A reduction to a piecewise constant intensity matrix function is proposed in order to provide succinct representations, where a parametric linear model binds the intensities together. Practical aspects are discussed and illustrated through the estimation of notoriously demanding theoretical distributions and real data, from the perspective of matrix analytic methods.
