Compound Poisson disorder problem with uniformly distributed disorder time

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buir.advisorDayanık, Savaş
dc.contributor.authorÜrü, Çağın
dc.date.accessioned2019-08-06T13:03:14Z
dc.date.available2019-08-06T13:03:14Z
dc.date.copyright2019-07
dc.date.issued2019-07
dc.date.submitted2019-07-26
dc.departmentDepartment of Industrial Engineeringen_US
dc.descriptionCataloged from PDF version of article.en_US
dc.descriptionThesis (M.S.): Bilkent University, Department of Industrial Engineering, İhsan Doğramacı Bilkent University, 2019.en_US
dc.descriptionIncludes bibliographical references (leaves 54-55).en_US
dc.description.abstractSuppose that arrival rate and jump distribution of a compound Poisson process change suddenly at an unknown and unobservable time. The problem of detecting the change (disorder) as soon as it occurs is known as compound Poisson disorder. In practice, an unfavorable regime shift may require immediate action, and a quickest detection rule can allow the decision maker to react to the change and take the necessary countermeasures in a timely manner. Dayanık and Sezer [Compound Poisson disorder problem, Math. Oper. Res., vol. 31, no. 4, pp. 649-672, 2006] completely solve the compound Poisson disorder problem assuming a change-point with an exponential prior distribution. Although the exponential prior is convenient when solving the problem, it has aws when expressing reality due to the memoryless property. Besides, as an informative prior, it fails to represent the case when the decision maker has no prior information on the change-point. Considering these defects, we assume a uniformly distributed change-point instead in our study. Unlike the exponential prior, the uniform prior has a memory and can be used when the decision maker does not have a strong belief on the change-point. We reformulate the quickest detection problem as a nite-horizon optimal stopping problem for a piecewisedeterministic and Markovian sufficient statistic. With Monte Carlo simulation and Chebyshev interpolation, we calculate the value function numerically via successive approximations. Studying the sample-paths of the sufficient statistic, we describe an explicit quickest detection rule and provide numerical examples for our solution method.en_US
dc.description.degreeM.S.en_US
dc.description.provenanceSubmitted by Betül Özen (ozen@bilkent.edu.tr) on 2019-08-06T13:03:14Z No. of bitstreams: 1 MS_Thesis_Çağın_Ürü.pdf: 1078173 bytes, checksum: ca7d74c3bba56ede1fe8dc94f086fbf2 (MD5)en
dc.description.provenanceMade available in DSpace on 2019-08-06T13:03:14Z (GMT). No. of bitstreams: 1 MS_Thesis_Çağın_Ürü.pdf: 1078173 bytes, checksum: ca7d74c3bba56ede1fe8dc94f086fbf2 (MD5) Previous issue date: 2019-07en
dc.description.statementofresponsibilityby Çağın Ürünen_US
dc.embargo.release2020-01-26
dc.format.extentix, 71 leaves ; 30 cm.en_US
dc.identifier.itemidB160103
dc.identifier.urihttp://hdl.handle.net/11693/52303
dc.language.isoEnglishen_US
dc.publisherBilkent Universityen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectPoisson disorder problemen_US
dc.subjectCompound poisson processen_US
dc.subjectQuickest detectionen_US
dc.subjectOptimal stoppingen_US
dc.titleCompound Poisson disorder problem with uniformly distributed disorder timeen_US
dc.title.alternativeTekdüze dağılan düzensizlik zamanlı bileşik Poisson düzensizlik problemien_US
dc.typeThesisen_US

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