Bayesian Analysis Of Regression Change-point Model Based On MCMC Algorithm

Change points are very common in industrial quality control,traffic data processing,financial analysis,weather simulation,software engineering and other fields.Therefore,how to estimate and detect these change points effectively has become one of the hot research directions in statistics in recent years.Linear regression model and dichotomous Probit regression model are widely used in various fields.It is a high value on theory and economy to Study the problem of change points.Therefore,basing on the change point theory and Bayesian method,MCMC sampling algorithm is used to study the change point estimation problem in these two regression models.The specific contents are as follows:Firstly,the basic theory of Bayesian method,MCMC algorithm,linear regression and Probit regression model are briefly analyzed and summarized.Secondly,based on the linear regression change-point model,the joint posterior distribution of unknown parameters such as change point position is obtained by Bayesian formula.The Bayesian estimation is obtained from the joint distribution.The sampling steps of MCMC algorithm are given,and R software is used for simulation.The results show that the estimation accuracy is high.Through empirical analysis,the reliability of the method is further illustrated.Thirdly,based on the general form of the Probit regression model,by introducing a Latent variable,the change point model of the Probit regression with potential variables is obtained.It can make the form and sampling of the joint posterior distribution simpler;From this distribution,the Bayesian estimation of each parameter is obtained.According to the steps of MCMC algorithm,R software is used for numerical simulation and empirical analysis.The results show that the Bayesian estimation effect is good.Finally,it summarizes the main research content and points out the future research direction.