A Bayesian Detection for the Number of Change Points in Linear Regression Model

利用貝氏方法偵測改變點個數於線性迴歸模型

10.6338/JDA.201510_10(5).0003

廖家儀(Chia-Yi Liao)；張國清(Kuo-Ching Chang)；李宗寶(Chung-Bow Lee)；江翠蓮(Chui-Liang Chiang)

改變點 ； 事後分配 ； 線性迴歸模型 ； Change points ； Posterior distribution ； Linear regression model

Journal of Data Analysis

10卷5期（2015 / 10 / 01）

49 - 78

英文

本文使用貝氏方法偵測改變點個數於線性迴歸模型。此為Fan et al.（1996）文章的推廣，從研究簡單線性迴歸到多維度線性迴歸，在分析中，將使用Normal-Gamma事前分配的迴歸參數，並推導出改變點位置及改變點個數的事後分配。在一些溫和的假設下，對於改變點個數及改變點位置的事後估計與真實改變點之間是有界性（Boundedness）而且一致性結果將被建構出。無論迴歸模型之轉折是否連續，利用貝氏方法去偵測改變點個數都是可行的。最後模擬結果將進行探討。

A Bayesian approach is considered to detect the number of change points in linear regression model. The work is the extension of that given by Fan et al. (1996) for simple linear regression. The normal-gamma prior information for the regression parameters is employed in the analysis. The marginal posterior distribution of the location of change points and the number of change points are derived. Under mild assumptions, con-sistency for the number of change points and boundedness between the posterior mode of the location and true location of change points are also established. The Bayesian approach for the detection of the number of change points is suitable whether the switching linear regression is continuous or discontinuous. Some simulat-ed results are given.

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