Optimal detection and diagnosis of an unobservable change in the distribution of a Markov-modulated random sequence
by
Christian Goulding
Princeton University
Coauthors: Savas Dayanik

Suppose that we observe sequentially the random variables X₁, X₂, ... whose finite-dimensional distribution changes at an unobservable disorder time T due to an unobservable cause A, which represents one of several competing risks. Our objective is to detect quickly this disorder and determine accurately its cause based only on the observation sequence. We approach this problem by modeling in a Bayesian framework the disorder time T, its cause A, and the distribution of the observation sequence X:={X_t;t ≥ 1}, as functionals of an underlying hidden Markov chain Y. We reveal an optimal solution and useful characteristics of its structure. We show how the classical sequential change detection and hypothesis-testing problems and recent extensions fit this formulation. Furthermore, we provide examples that illustrate the myriad of sequential change detection and diagnosis problems that fall within this new framework.

Date received: February 27, 2007