﻿ 正态分布下多个方差转变点的检测与方法探讨 A Method of Detecting Multiple Change Point for Normal Distribution Process

Vol.05 No.03(2016), Article ID:18238,6 pages
10.12677/AAM.2016.53040

A Method of Detecting Multiple Change Point for Normal Distribution Process

Huihui Shen1,2

1Hubei University of Economics, Wuhan Hubei

2China University of Geosciences, Wuhan Hubei

Received: Jul. 20th, 2016; accepted: Aug. 12th, 2016; published: Aug. 15th, 2016

ABSTRACT

The problem of structure model occurs multiple change points in the economic system of mathematical models. In this paper, we give the detection method for change point problems about the variance changes. We combine the Bayesian method with the maximum likelihood method on the detection about the variance multiple change points in the same mean. The elimination extra parameters can make use of Bayesian method; the maximum likelihood method can avoid the unknown problems of the prior distribution information of the change points number. It is a practical method.

Keywords:Change Point, Bayesian Method, Maximum Likelihood Method, Prior Distribution, Likelihood Density Function

1湖北经济学院，湖北 武汉

2中国地质大学，湖北 武汉

1. 引言

2. 方差转变点的检测

Shao 和 Hou (2006) [15] 运用S—控制图和极大似然方法相结合来估计服从gamma分布的随机变量的转变点问题。Wenzhi Zhao, Zheng Tian, Zhiming Xia (2010) [16] 针对有长期记忆的线性过程用比值判别法来检测方差转变点，但是此方法需要一定的限制假设条件。文献 [17] 结合了X控制图与贝叶斯估计方法，文献 [18] 的应用实证中也运用贝叶斯方法来定位找到转变点的位置，通过一系列模拟。结果表明，贝叶斯估计量与之前的信息更准确和更精确。

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2.1. 贝叶斯检测

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2.2. 极大似然方法检测

A Method of Detecting Multiple Change Point for Normal Distribution Process[J]. 应用数学进展, 2016, 05(03): 321-326. http://dx.doi.org/10.12677/AAM.2016.53040

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