Quickest detection of intensity change for Poisson process in generalized Bayesian setting
نویسنده
چکیده
The paper deals with the quickest detection of intensity change for Poisson process. We show that the generalized Bayesian formulation of the quickest detection problem can be reduced to the conditional-extremal optimal stopping problem for a piecewise-deterministic Markov process. For this problem the optimal procedure is described and its characteristics are found.
منابع مشابه
Bayesian change point estimation in Poisson-based control charts
Precise identification of the time when a process has changed enables process engineers to search for a potential special cause more effectively. In this paper, we develop change point estimation methods for a Poisson process in a Bayesian framework. We apply Bayesian hierarchical models to formulate the change point where there exists a step < /div> change, a linear trend and a known multip...
متن کاملQuickest Detection of Drift Change for Brownian Motion in Generalized Bayesian and Minimax Settings
The paper deals with the quickest detection of a change of the drift of the Brownian motion. We show that the generalized Bayesian formulation of the quickest detection problem can be reduced to the optimal stopping problem for a diffusion Markov process. For this problem the optimal procedure is described and its characteristics are found. We show also that the same procedure is asymptotically...
متن کاملAsymptotically Optimal Quickest Change Detection in Distributed Sensor Systems
In the standard formulation of the quickest change-point detection problem, a sequence of observations, whose distribution changes at some unknown point in time, is available to a decision maker, and the goal is to detect this change as quickly as possible, subject to false alarm constraints. In this paper, we study the quickest change detection problem in the setting where the information avai...
متن کاملدربارۀ شناسایی بیزیِ دنبالهای نقطۀ تغییر
The problems of sequential change-point have several important applications in quality control, signal processing, and failure detection in industry and finance and signal detection. We discuss a Bayesian approach in the context of statistical process control: at an unknown time τ, the process behavior changes and the distribution of the data changes from p0 to p1. Two cases are consi...
متن کاملBayesian Quickest Transient Change Detection
We consider the problem of quickest transient change detection under a Bayesian setting. The change occurs at a random time Γ1 and disappears at a random time Γ2 > Γ1. Thus, at any time k, the system can be in one of the following states, i) prechange, ii) in–change, and iii) out–of–change. We model the evolution of the state by a Markov chain. The state of the system can only be observed parti...
متن کامل