Mathematics – Optimization and Control
Scientific paper
2006-11-19
Mathematics
Optimization and Control
Scientific paper
We consider a change detection problem in which the arrival rate of a Poisson process changes suddenly at some unknown and unobservable disorder time. It is assumed that the prior distribution of the disorder time is known. The objective is to detect the disorder time with an online detection rule (a stopping time) in a way that balances the frequency of false alarm and detection delay. So far in the study of this problem, the prior distribution of the disorder time is taken to be exponential distribution for analytical tractability. Here, we will take the prior distribution to be a phase-type distribution, which is the distribution of the absorption time of a continuous time Markov chain with a finite state space. We find an optimal stopping rule for this general case and give a numerical algorithm that calculates the parameters of $\eps$-optimal strategies for any $\eps>0$. We illustrate our findings on two examples.
Bayraktar Erhan
Sezer Semih
No associations
LandOfFree
Quickest Detection for a Poisson Process with a Phase-type Change-time Distribution does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Quickest Detection for a Poisson Process with a Phase-type Change-time Distribution, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quickest Detection for a Poisson Process with a Phase-type Change-time Distribution will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-419955