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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Bibliographic Details
Published in:Mathematics of operations research Vol. 31; no. 4; pp. 649 - 672
Main Authors: Dayanik, Savas, Sezer, Semih Onur
Format: Journal Article
Language:English
Published: Linthicum INFORMS 01.11.2006
Institute for Operations Research and the Management Sciences
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0364-765X
1526-5471
DOI:10.1287/moor.1060.0223