Bayesian Estimation of the Number of Change Points in Simple Linear Regression Models

A Bayesian approach is considered to detect the number of change points in simple linear regression models. A normal-gamma empirical prior for the regression parameters based on maximum likelihood estimator (MLE) is employed in the analysis. Under mild conditions, consistency for the number of change points and boundedness between the estimated location and the true location of the change points are established. The Bayesian approach to the detection of the number of change points is suitable whether the switching simple regression is continuous or discontinuous. Some simulation results are given to confirm the accuracy of the proposed estimator.

Keywords:

• Bayesian estimation
• Change points
• Consistency
• Linear regression

Mathematics Subject Classification:

• 62F15
• 62J05

Acknowledgments

The authors would like to thank the referee for his help in improving this article. This work was partially supported by the MOE program for promoting academic excellent of universities under grant number 91-H-FA07-1-4.