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Article: How to count and guess well: Discrete adaptive filters

TitleHow to count and guess well: Discrete adaptive filters
Authors
KeywordsAms Classification: 93E11, 93E12, 60G35
Discrete Adaptive Filter
Expectation Maximization
Girsanov Theorem
Hidden Markov Model
Martingale
Representation
Smoothed Estimate
Zakai Equation
Issue Date1994
PublisherSpringer New York LLC. The Journal's web site is located at http://link.springer.de/link/service/journals/00245/
Citation
Applied Mathematics & Optimization, 1994, v. 30 n. 1, p. 51-78 How to Cite?
AbstractA discrete state and time Markov chain is observed through a finite state function which is subject to random perturbations. Such a situation is often called a Hidden Markov Model. A general filter is obtained which provides recursive updates of estimates of processes related to the Markov chain given the observations. In the unnormalized, or Zakai, form this provides particularly simple equations. Specializing this result provides recursive estimates and smoothers for the state of the process, for the number of jumps from one state to another, for the occupation time in any state and for a process related to the observations. These results allow a re-estimation of the parameters of the model, so that our procedures are adaptive or "self tuning" to the data. The main contributions of this paper are the introduction of an equivalent measure under which the observation values are independent and identically distributed, and the use of the idempotent property when the state space of the Markov chain is identified with canonical unit vectors in a Euclidean space. © 1994 Springer-Verlag New York Inc.
Persistent Identifierhttp://hdl.handle.net/10722/172367
ISSN
2015 Impact Factor: 1.366
2015 SCImago Journal Rankings: 0.955

 

DC FieldValueLanguage
dc.contributor.authorElliott, RJen_US
dc.contributor.authorYang, Hen_US
dc.date.accessioned2012-10-30T06:22:10Z-
dc.date.available2012-10-30T06:22:10Z-
dc.date.issued1994en_US
dc.identifier.citationApplied Mathematics & Optimization, 1994, v. 30 n. 1, p. 51-78en_US
dc.identifier.issn0095-4616en_US
dc.identifier.urihttp://hdl.handle.net/10722/172367-
dc.description.abstractA discrete state and time Markov chain is observed through a finite state function which is subject to random perturbations. Such a situation is often called a Hidden Markov Model. A general filter is obtained which provides recursive updates of estimates of processes related to the Markov chain given the observations. In the unnormalized, or Zakai, form this provides particularly simple equations. Specializing this result provides recursive estimates and smoothers for the state of the process, for the number of jumps from one state to another, for the occupation time in any state and for a process related to the observations. These results allow a re-estimation of the parameters of the model, so that our procedures are adaptive or "self tuning" to the data. The main contributions of this paper are the introduction of an equivalent measure under which the observation values are independent and identically distributed, and the use of the idempotent property when the state space of the Markov chain is identified with canonical unit vectors in a Euclidean space. © 1994 Springer-Verlag New York Inc.en_US
dc.languageengen_US
dc.publisherSpringer New York LLC. The Journal's web site is located at http://link.springer.de/link/service/journals/00245/en_US
dc.relation.ispartofApplied Mathematics & Optimizationen_US
dc.subjectAms Classification: 93E11, 93E12, 60G35en_US
dc.subjectDiscrete Adaptive Filteren_US
dc.subjectExpectation Maximizationen_US
dc.subjectGirsanov Theoremen_US
dc.subjectHidden Markov Modelen_US
dc.subjectMartingaleen_US
dc.subjectRepresentationen_US
dc.subjectSmoothed Estimateen_US
dc.subjectZakai Equationen_US
dc.titleHow to count and guess well: Discrete adaptive filtersen_US
dc.typeArticleen_US
dc.identifier.emailYang, H: hlyang@hku.hken_US
dc.identifier.authorityYang, H=rp00826en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1007/BF01261991en_US
dc.identifier.scopuseid_2-s2.0-0004235294en_US
dc.identifier.volume30en_US
dc.identifier.issue1en_US
dc.identifier.spage51en_US
dc.identifier.epage78en_US
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridElliott, RJ=7402639776en_US
dc.identifier.scopusauthoridYang, H=7406559537en_US
dc.identifier.citeulike8211155-

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