基于差分进化算法的正态分布均值变点检测

变点是指从某个时刻开始,样本的分布或数字特征发生变化。该文研究已知变点个数条件下的正态分布序列均值变点位置的检测问题。根据贝叶斯理论,对变点参数和均值参数取无信息先验分布,得到变点位置的后验分布,为计算后验分布,应用差分进化算法(DE)和自适应差分进化算法(ADE)对后验分布进行研究,并进行数值模拟。实验结果表明,2种算法均能够快速有效地估计正态分布序列中均值变点的位置。其中,差分进化算法的估计效果较自适应差分进化算法更好。

Change-point is a change in the distribution or numerical characteristics of a sample from a certain point.In this paper,we study the problem of detecting the position of the mean change points of a normally distributed series with a given number of change points.According to Bayesian theory,non-informative prior distribution was taken for the parameters of the change point and the mean value,and a posteriori distribution of the position of the change point was obtained.In order to calculate the posteriori distribution,Differential Evolution Algorithm(DE)and Adaptive Differential Evolution Algorithm(ADE)were used to study the posteriori distribution and perform numerical simulation.The experimental results show that both algorithms can estimate the position of mean change point in normally distributed sequences quickly and effectively.Among them,the Differential Evolution Algorithm has better estimation effect than the Adaptive Differential Evolution Algorithm.