Compound Poisson Disorder Problem

In the compound Poisson disorder problem, arrival rate and/or jump distribution of some compound Poisson process changes suddenly at some unknown and unobservable time. The problem is to detect the change (or disorder) time as quickly as possible. A sudden regime shift may require some countermeasur...

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Vydáno v:Mathematics of operations research Ročník 31; číslo 4; s. 649 - 672
Hlavní autoři: Dayanik, Savas, Sezer, Semih Onur
Médium: Journal Article
Jazyk:angličtina
Vydáno: Linthicum INFORMS 01.11.2006
Institute for Operations Research and the Management Sciences
Témata:
Analysis
Approximation
Bayesian analysis
Bayesian statistical decision theory
Chromosome disorders
compound Poisson processes
Determinism
Equations
Markov processes
Mathematical constants
Mathematical functions
Mathematical models
Mathematics
optimal stopping
Poisson disorder problem
Poisson distribution
Poisson equation
quickest detection
Random variables
Stopping distances
Studies
Study and teaching
ISSN:0364-765X, 1526-5471
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Abstract In the compound Poisson disorder problem, arrival rate and/or jump distribution of some compound Poisson process changes suddenly at some unknown and unobservable time. The problem is to detect the change (or disorder) time as quickly as possible. A sudden regime shift may require some countermeasures be taken promptly, and a quickest detection rule can help with those efforts. We describe complete solution of the compound Poisson disorder problem with several standard Bayesian risk measures. Solution methods are feasible for numerical implementation and are illustrated by examples.
AbstractList In the compound Poisson disorder problem, arrival rate and/or jump distribution of some compound Poisson process changes suddenly at some unknown and unobservable time. The problem is to detect the change (or disorder) time as quickly as possible. A sudden regime shift may require some countermeasures be taken promptly, and a quickest detection rule can help with those efforts. We describe complete solution of the compound Poisson disorder problem with several standard Bayesian risk measures. Solution methods are feasible for numerical implementation and are illustrated by examples.
In the compound Poisson disorder problem, arrival rate and/or jump distribution of some compound Poisson process changes suddenly at some unknown and unobservable time. The problem is to detect the change (or disorder) time as quickly as possible. A sudden regime shift may require some countermeasures be taken promptly, and a quickest detection rule can help with those efforts. We describe complete solution of the compound Poisson disorder problem with several standard Bayesian risk measures. Solution methods are feasible for numerical implementation and are illustrated by examples. [PUBLICATION ABSTRACT]
Audience Academic
Author Sezer, Semih Onur
Dayanik, Savas
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Cites_doi 10.1016/j.spa.2005.04.011
10.1524/stnd.22.1.79.32716
10.1007/978-1-4684-9477-8
10.1111/j.2517-6161.1984.tb01308.x
10.1007/978-1-4899-4483-2
10.1080/17442508608833426
10.4064/-1-1-65-72
10.1007/978-1-4757-2341-0
10.1007/978-3-662-04790-3_16
10.1287/moor.1060.0190
10.1214/105051604000000981
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SubjectTerms Analysis
Approximation
Bayesian analysis
Bayesian statistical decision theory
Chromosome disorders
compound Poisson processes
Determinism
Equations
Markov processes
Mathematical constants
Mathematical functions
Mathematical models
Mathematics
optimal stopping
Poisson disorder problem
Poisson distribution
Poisson equation
quickest detection
Random variables
Stopping distances
Studies
Study and teaching
Title Compound Poisson Disorder Problem
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