Compound poisson disorder problems with nonlinear detection delay penalty cost functions
Author
Dayanik, S.
Date
2010Source Title
Sequential Analysis
Print ISSN
0747-4946
Volume
29
Issue
2
Pages
193 - 216
Language
English
Type
ArticleItem Usage Stats
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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.
Keywords
Bayesian sequential change detectionCompound 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