Compound poisson disorder problems with nonlinear detection delay penalty cost functions

Date
2010
Authors
Dayanik, S.
Advisor
Instructor
Source Title
Sequential Analysis
Print ISSN
0747-4946
Electronic ISSN
Publisher
Volume
29
Issue
2
Pages
193 - 216
Language
English
Type
Article
Journal Title
Journal ISSN
Volume Title
Abstract

The quickest detection of the unknown and unobservable disorder time, when the arrival rate and mark distribution of a compound Poisson process suddenly changes, is formulated in a Bayesian setting, where the detection delay penalty is a general smooth function of the detection delay time. Under suitable conditions, the problem is shown to be equivalent to the optimal stopping of a finite-dimensional piecewise-deterministic strongly Markov sufficient statistic. The solution of the optimal stopping problem is described in detail for the compound Poisson disorder problem with polynomial detection delay penalty function of arbitrary but fixed degree. The results are illustrated for the case of the quadratic detection delay penalty function. © Taylor & Francis Group, LLC.

Course
Other identifiers
Book Title
Keywords
Bayesian sequential change detection, Compound poisson disorder problem, Optimal stopping, Piecewise-deterministic markov processes, Compound poisson, Compound Poisson process, Optimal stopping, Optimal stopping problem, Piecewise deterministic Markov process, Sequential change detection, Sufficient statistics, Suitable conditions, Polynomials, Optimization
Citation
Published Version (Please cite this version)