On the Optimal Sequential Detection of Change Points

• Activity Number: 403
• Type: Contributed
• Date/Time: Thursday, August 15, 2002 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Stat. Sciences*
• Author(s): Michael Barón*+
• Affiliation(s): University of Texas, Dallas
• Keywords: Change point ; sequential ; Bayes ; stopping rule ; hidden Markov chain

Abstract

In sequential change-point analysis, it is desirable to detect a change in distribution as soon as possible after it occurs, while keeping the rate of false alarms to a minimum. Most of the change points occur unexpectedly, at random times, justifying the need of Bayesian procedures.

Objective prior distributions of change point parameters can be constructed based on a number of factors, and they usually take rather complicated forms. Often the whole prior distribution of a change point is not known, and only the current value of its discrete hazard rate function is available.

On the other hand, only in certain specific cases is it possible to construct Bayes sequential rules for change-point detection. The general form of a Bayes sequential rule has not been obtained.

We derive the Bayes scheme for the situation when the hazard rate of a change point is determined by a homogeneous Markov process. This provides the Bayes solution to a so-called decoding problem for hidden Markov chains. In a more general setting, we propose asymptotically pointwise optimal procedures for an arbitrary prior. Another general procedure is derived from a sequence of Bayes tests.