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Article: How to count and guess well: Discrete adaptive filters
Title | How to count and guess well: Discrete adaptive filters |
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Authors | |
Keywords | Ams Classification: 93E11, 93E12, 60G35 Discrete Adaptive Filter Expectation Maximization Girsanov Theorem Hidden Markov Model Martingale Representation Smoothed Estimate Zakai Equation |
Issue Date | 1994 |
Publisher | Springer 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? |
Abstract | A 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 Identifier | http://hdl.handle.net/10722/172367 |
ISSN | 2021 Impact Factor: 2.194 2020 SCImago Journal Rankings: 0.913 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Elliott, RJ | en_US |
dc.contributor.author | Yang, H | en_US |
dc.date.accessioned | 2012-10-30T06:22:10Z | - |
dc.date.available | 2012-10-30T06:22:10Z | - |
dc.date.issued | 1994 | en_US |
dc.identifier.citation | Applied Mathematics & Optimization, 1994, v. 30 n. 1, p. 51-78 | en_US |
dc.identifier.issn | 0095-4616 | en_US |
dc.identifier.uri | http://hdl.handle.net/10722/172367 | - |
dc.description.abstract | A 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.language | eng | en_US |
dc.publisher | Springer New York LLC. The Journal's web site is located at http://link.springer.de/link/service/journals/00245/ | en_US |
dc.relation.ispartof | Applied Mathematics & Optimization | en_US |
dc.subject | Ams Classification: 93E11, 93E12, 60G35 | en_US |
dc.subject | Discrete Adaptive Filter | en_US |
dc.subject | Expectation Maximization | en_US |
dc.subject | Girsanov Theorem | en_US |
dc.subject | Hidden Markov Model | en_US |
dc.subject | Martingale | en_US |
dc.subject | Representation | en_US |
dc.subject | Smoothed Estimate | en_US |
dc.subject | Zakai Equation | en_US |
dc.title | How to count and guess well: Discrete adaptive filters | en_US |
dc.type | Article | en_US |
dc.identifier.email | Yang, H: hlyang@hku.hk | en_US |
dc.identifier.authority | Yang, H=rp00826 | en_US |
dc.description.nature | link_to_subscribed_fulltext | en_US |
dc.identifier.doi | 10.1007/BF01261991 | en_US |
dc.identifier.scopus | eid_2-s2.0-0004235294 | en_US |
dc.identifier.volume | 30 | en_US |
dc.identifier.issue | 1 | en_US |
dc.identifier.spage | 51 | en_US |
dc.identifier.epage | 78 | en_US |
dc.identifier.isi | WOS:A1994NK77300004 | - |
dc.publisher.place | United States | en_US |
dc.identifier.scopusauthorid | Elliott, RJ=7402639776 | en_US |
dc.identifier.scopusauthorid | Yang, H=7406559537 | en_US |
dc.identifier.citeulike | 8211155 | - |
dc.identifier.issnl | 0095-4616 | - |