Change-point models and performance measures for sequential change detection

For the problem of sequential change detection we propose a novel modelling of the change-point mechanism. In particular we regard the time of change as a stopping time controlled by Nature. Nature, in order to decide when to impose the change, accesses sequentially information which can be different from the information provided to the Statistician to detect the change. Using as performance measure the classical conditional detection delay, we recover most well known criteria of the literature by considering different dependency classes between the information accessed by Nature and the information accessed by the Statistician. According to our approach, the Shiryaev and Pollak measure correspond to informations that are completely independent while in Lorden’s measure the two informations must coincide. By considering alternative models between these two extreme scenarios, we obtain a number of completely new criteria.