1-4 September 2015
Angers - France
Europe/Paris timezone

Robust Detection of Unobservable Disorder in Poisson rate

4 Sep 2015, 09:00
40m
Angers - France

Angers - France

Speaker

Prof. Nicole El Karoui (UPMC)

Description

We consider the non-Bayesian quickest detection problem of an unobservable time of change in the rate of an inhomogeneous Poisson process. We seek a stopping rule that minimizes the robust Lorden criterion. The latter is formulated in terms of the number of events until detection, both for the worst-case delay and the false alarm constraint. In the Wiener case, such a problem was solved using the so- called cumulative sums (cusum) strategy by many authors (Moustakides (2004), or Shyraiev (1963,..2009)). In our setting, we derive the exact optimality of the cusum stopping rule by using finite variation calculus and elementary martingale properties to characterize the performance functions of the cusum stopping rule in terms of scale function. These are solutions of some delayed differential equations that we solve elementary. The case of detecting a decrease in the intensity is easy to study because the performance functions are continuous. In case of increase where the performance functions are not continuous, martingale properties require using a discontinuous local time. Nevertheless, from an identity relating the scale functions, the optimality of the cusum rule still holds. Numerical applications are provided. This is joint work with S.Loisel (ISFA) and Y.Sahli (ISFA).

Primary author

Prof. Nicole El Karoui (UPMC)

Presentation Materials