论文标题
多元Lévy型漂移变化检测和死亡率建模
Multivariate Lévy-type drift change detection and mortality modeling
论文作者
论文摘要
在本文中，我们为贝叶斯方法中的连续（高斯）和跳跃成分组成的多变量lévy过程提供了最快的漂移变化检测问题。我们为变更点的一般性连续分布进行了一般的连续分布。从经典上讲，我们的最优标准是基于错误警报的概率和检测的预期延迟，然后根据变化点的后验概率对其进行重新进行重新重新审核。我们发现后验概率的发生器，如果一般的先验分布在时间上是不均匀的。主要解决技术使用最佳停止理论，并基于解决某些自由边界问题。我们还构建了一个通用的Shiryaev-Roberts统计量，可用于应用程序。该论文补充了两个例子，其中一个进一步用于分析波兰寿命表（适当校准后），并检测到共同死亡力的相关力的漂移变化。
In this paper we give a solution to the quickest drift change detection problem for a multivariate Lévy process consisting of both continuous (Gaussian) and jump components in the Bayesian approach. We do it for a general 0-modified continuous prior distribution of the change point. Classically, our criterion of optimality is based on a probability of false alarm and an expected delay of the detection, which is then reformulated in terms of a posterior probability of the change point. We find a generator of the posterior probability, which in case of general prior distribution is inhomogeneous in time. The main solving technique uses the optimal stopping theory and is based on solving a certain free-boundary problem. We also construct a Generelized Shiryaev-Roberts statistic, which can be used for applications. The paper is supplemented by two examples, one of which is further used to analyze Polish life tables (after proper calibration) and detect the drift change in the correlated force of mortality of men and women jointly.
