SURVEY OF CLASSICAL AND BAYESIAN APPROACHES TO THE CHANGE-POINT PROBLEM: FIXED SAMPLE AND SEQUENTIAL PROCEDURES OF TESTING AND ESTIMATION

Abstract

This chapter discusses fixed sample and the sequential procedures of testing and estimation and describes classical and Bayesian approaches to the change-point problem. It presents Bayesian and maximum likelihood estimation of the location of the shift points. The Bayesian approach is based on modeling the prior distribution of the unknown parameters, adopting a loss function and deriving the estimator, which minimizes the posterior risk. The chapter discusses this approach with an example of a shift in the mean of a normal sequence. The estimators obtained are generally nonlinear complicated functions of the random variables. From the Bayesian point of view, these estimators are optimal. The maximum likelihood estimation of the location parameter of the change point is an attractive alternative to the Bayes estimators. Regression relationship can change at unknown epochs, resulting in different regression regimes that should be detected and identified.