Joint Detection and Identification of an Unobservable Change in the Distribution of a Random Sequence

TL;DR

This paper introduces an optimal Bayesian sequential decision strategy for the joint detection and identification of unobservable distribution changes in i.i.d. sequences, enhancing quick detection and accurate inference.

Contribution

It proposes a novel Bayesian approach with a proven optimal strategy for simultaneous change detection and identification in distributional shifts.

Findings

The strategy is proven to be optimal.

Numerical examples demonstrate the geometrical properties.

The method improves detection speed and accuracy.

Abstract

This paper examines the joint problem of detection and identification of a sudden and unobservable change in the probability distribution function (pdf) of a sequence of independent and identically distributed (i.i.d.) random variables to one of finitely many alternative pdf's. The objective is quick detection of the change and accurate inference of the ensuing pdf. Following a Bayesian approach, a new sequential decision strategy for this problem is revealed and is proven optimal. Geometrical properties of this strategy are demonstrated via numerical examples.