Model misspecification in discrete time bayesian online change detection

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buir.contributor.authorDayanik, Semih
buir.contributor.orcidDayanik, Semih|0000-0002-0810-5507
dc.citation.epage27en_US
dc.citation.issueNumber1
dc.citation.spage1
dc.citation.volumeNumber25
dc.contributor.authorDayanik, Semih
dc.contributor.authorSezer, Semih O
dc.date.accessioned2024-03-05T11:14:22Z
dc.date.available2024-03-05T11:14:22Z
dc.date.issued2023-02-17
dc.departmentDepartment of Industrial Engineering
dc.description.abstractWe revisit the classical formulation of the discrete time Bayesian online change detection problem in which the common distribution of an observed sequence of random variables changes at an unknown point in time. The objective is to detect the change with a stopping time of the observations and minimize a given Bayes risk. When the change time has a zero-modified geometric prior distribution, the first crossing time of the odds-ratio process over a threshold is known to be an optimal solution. In the current paper, we consider a modeler who misspecifies some of the elements of this formulation. Because of this misspecification, the modeler computes a wrong stopping threshold and follows an incorrect odds-ratio process in implementation. To find her actual Bayes risk, which is different from the value function evaluated with the wrong choices, one needs to compute the expected costs accumulated by the true odds-ratio process until modeler’s odd-ratio process crosses this wrong boundary. In the paper, we carry out these computations in the extended state space of both processes, and we illustrate these computations on examples. In those examples, we construct tolerance regions for the parameters to be estimated by the modeler. For a given choice by the modeler, the tolerance region is the set of true values for which her relative loss is less than or equal to a predetermined level.
dc.identifier.doi10.1007/s11009-023-09991-4
dc.identifier.eissn1573-7713
dc.identifier.issn1387-5841
dc.identifier.urihttps://hdl.handle.net/11693/114347
dc.language.isoen
dc.publisherSpringer
dc.relation.isversionofhttps://dx.doi.org/10.1007/s11009-023-09991-4
dc.rightsCC BY 4.0 Deed (Attribution 4.0 International)
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.source.titleMethodology and Computing in Applied Probability
dc.subjectBayesian quickest detection
dc.subjectOptimal stopping
dc.subjectSequential analysis
dc.titleModel misspecification in discrete time bayesian online change detection
dc.typeArticle

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