0-1序列中变点的贝叶斯分析

Bayesian Analysis of Change-Points in 0-1 Sequences

对于0-1(伯努利)序列中的变点问题,本文提出了一个确定变点的个数和位置的贝叶斯方法。首先借助于二分法把变点个数的确定问题转化为一系列对没有变点和仅有一个变点的模型进行比较的问题,然后通过贝叶斯因子进行模型比较。本文得到了贝叶斯因子和未知变点的后验分布的显式表达式。最后,通过对上证指数数据的实证分析阐释了所提方法的有效性。

This paper proposed a Bayesian statistical method to determine the number and locations of change points in a 0-1 sequence. Based on a binary segmentation procedure, we first transformed the problem of determining the number of change points into a series of problems of comparing model with no change point and one with only one change point, and then conducted model comparison by means of Bayes factor. We also obtained closed-form formula of the Bayes factor and the posterior distribution of the change point. The empirical analyzed results of Shanghai composite index data illustrated the effectiveness of the proposed method.