  The problem of detecting changes in the statistical properties of a
stochastic system and time series arises in various branches of science and
engineering. It has a wide spectrum of important applications ranging from
machine monitoring to biomedical signal processing. In all of these
applications the observations being monitored undergo a change in distribution
in response to a change or anomaly in the environment, and the goal is to
detect the change as quickly as possibly, subject to false alarm constraints.
In this chapter, two formulations of the quickest change detection problem,
Bayesian and minimax, are introduced, and optimal or asymptotically optimal
solutions to these formulations are discussed. Then some generalizations and
extensions of the quickest change detection problem are described. The chapter
is concluded with a discussion of applications and open issues.
