Sequential detection of transient changes (the case of dynamic profile)
Résumé
This presentation addresses the problem of transient change detection. It is assumed that the duration of a transient change is usually short. In contrast to the conventional abrupt change detection, where the post-change period is assumed to be infinitely long, the detection of a transient change should be done before it disappears. The alert about the transient changes after their disappearance is considered as a missed detection. Often, such a transient change is represented by a dynamic profile in the parameter space. The conventional quickest change detection criterion, minimizing the average detection delay provided that a false alarm rate is upper bounded, cannot be used now and another optimality criterion which minimizes the worst-case probability of missed detection provided that the worst-case prob- ability of false alarm during a certain period is upper bounded is used for a transient change detection. A special attention will be paid to the case of arbitrary (non-Gaussian) distribution of observations. A special continuous-discrete model with tran- sient changes will be also considered. Finally, several possible applications of the proposed tests will be presented.