Cusum和Shiryaev-Roberts方法检测分布变化的数值比较
Numerical Comparison of Cusum and Shiryaev-Roberts Procedures for Detecting Changes in Distributions
摘要：
众所周知，在极大极小情形下，最佳的检测分布变化的过程是，而Shiryaev-Roberts过程是最佳的检测发生在遥远的时间范围内的变化。作为传统的蒙特卡罗方法的一种更简单的替代方法，我们提出了一种数值方法，用于在两种设置中系统地比较两种检测方案，即，minimax和用于检测在遥远的未来发生的变化。我们的目标是通过推导出一组精确的积分方程的性能指标，然后数值求解。我们提出了详细的数值计算结果的问题，检测高斯序列的平均值的变化，这表明这两个程序之间的差异是显着的，只有当检测到小的变化。
英文摘要：
The CUSUM procedure is known to be optimal for detecting a change in distribution under a minimax scenario, whereas the Shiryaev-Roberts procedure is optimal for detecting a change that occurs at a distant time horizon. As a simpler alternative to the conventional Monte Carlo approach, we propose a numerical method for the systematic comparison of the two detection schemes in both settings, i.e., minimax and for detecting changes that occur in the distant future. Our goal is accomplished by deriving a set of exact integral equations for the performance metrics, which are then solved numerically. We present detailed numerical results for the problem of detecting a change in the mean of a Gaussian sequence, which show that the difference between the two procedures is significant only when detecting small changes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
