Semi-Markov chains and hidden semi-Markov models toward applications: their use in reliability and DNA analysis
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New York, NY
Springer
2008
|
| Schriftenreihe: | Lecture notes in statistics
191 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016778218&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XIII, 224 S. graph. Darst. 235 mm x 155 mm |
| ISBN: | 9780387731711 0387731717 9780387731735 |
Internformat
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| 245 | 1 | 0 | |a Semi-Markov chains and hidden semi-Markov models toward applications |b their use in reliability and DNA analysis |c Vlad Stefan Barbu ; Nikolaos Limnios |
| 264 | 1 | |a New York, NY |b Springer |c 2008 | |
| 300 | |a XIII, 224 S. |b graph. Darst. |c 235 mm x 155 mm | ||
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| 490 | 1 | |a Lecture notes in statistics |v 191 | |
| 650 | 4 | |a ADN - Analyse - Modèles mathématiques | |
| 650 | 4 | |a Fiabilité - Modèles mathématiques | |
| 650 | 4 | |a Processus de Markov | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a DNA |x Analysis |x Mathematics | |
| 650 | 4 | |a DNA |x Mathematical models | |
| 650 | 4 | |a DNA |x analysis | |
| 650 | 4 | |a Markov Chains | |
| 650 | 4 | |a Markov processes | |
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Datensatz im Suchindex
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| adam_text | Contents
Preface........................................................ VII
1 Introduction............................................... 1
1.1 Object of the Study ..................................... 1
1.1.1 The Underlying Idea in Semi-Markov Models......... 1
1.1.2 Discrete Time..................................... 4
1.2 Discrete-Time Semi-Markov Framework.................... 5
1.2.1 Discrete-Time Renewal Processes.................... 5
1.2.2 Semi-Markov Chains............................... 7
1.2.3 Semi-Markov Chain Estimation..................... 10
1.3 Reliability Theory of Discrete-Time Semi-Markov Systems .... 11
1.4 Hidden Semi-Markov Models.............................. 13
2 Discrete-Time Renewal Processes ......................... 17
2.1 Renewal Chains......................................... 18
2.2 Limit Theorems......................................... 26
2.3 Delayed Renewal Chains ................................. 31
2.4 Alternating Renewal Chain............................... 37
Exercises ................................................... 40
3 Semi-Markov Chains ...................................... 43
3.1 Markov Renewal Chains and Semi-Markov Chains........... 44
3.2 Markov Renewal Theory ................................. 51
3.3 Limit Theorems for Markov Renewal Chains................ 60
3.4 Periodic SMC........................................... 67
3.5 Monte Carlo Methods.................................... 67
3.6 Example: a Textile Factory............................... 68
Exercises ................................................... 73
XII Contents
4 Nonparametric Estimation for Semi-Markov Chains....... 75
4.1 Construction of the Estimators............................ 76
4.2 Asymptotic Properties of the Estimators................... 79
4.3 Example: a Textile Factory (Continuation) ................. 95
Exercises ................................................... 98
5 Reliability Theory for Discrete-Time Semi-Markov Systems 101
5.1 Reliability Function and Associated Measures...............102
5.1.1 Reliability........................................104
5.1.2 Availability.......................................106
5.1.3 Maintainability ...................................108
5.1.4 Failure Rates.....................................108
5.1.5 Mean Hitting Times...............................Ill
5.2 Nonparametric Estimation of Reliability....................115
5.3 Example: a Textile Factory (Continuation) .................122
Exercises ...................................................129
6 Hidden Semi-Markov Model and Estimation...............131
6.1 Hidden Semi-Markov Model ..............................132
6.2 Estimation of a Hidden Semi-Markov Model................136
6.2.1 Consistency of Maximum-Likelihood Estimator.......137
6.2.2 Asymptotic Normality of Maximum-Likelihood
Estimator........................................144
6.3 Monte Carlo Algorithm..................................150
6.4 EM Algorithm for a Hidden Semi-Markov Model............151
6.4.1 Preliminaries .....................................151
6.4.2 EM Algorithm for Hidden Model SM-M0.............153
6.4.3 EM Algorithm for Hidden Model SM-M1.............158
6.4.4 Proofs...........................................163
6.4.5 Example: CpG Island Detection.....................173
Exercises ...................................................177
A Lemmas for Semi-Markov Chains..........................179
B Lemmas for Hidden Semi-Markov Chains..................183
B.I Lemmas for Hidden SM-M0 Chains........................183
B.2 Lemmas for Hidden SM-M1 Chains........................184
C Some Proofs...............................................185
D Markov Chains............................................195
D.I Definition and Transition Function ........................195
D.2 Strong Markov Property..................................197
D.3 Recurrent and Transient States............................197
D.4 Stationary Distribution...................................199
D.5 Markov Chains and Reliability............................200
Contents XIII
E Miscellaneous..............................................203
Notation.......................................................207
References.....................................................211
Index..........................................................221
|
| any_adam_object | 1 |
| author | Barbu, Vlad Stefan Limnios, Nikolaos |
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| discipline | Mathematik |
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| id | DE-604.BV035110382 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T13:20:25Z |
| institution | BVB |
| isbn | 9780387731711 0387731717 9780387731735 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016778218 |
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| owner_facet | DE-824 DE-19 DE-BY-UBM DE-83 DE-11 |
| physical | XIII, 224 S. graph. Darst. 235 mm x 155 mm |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in statistics |
| series2 | Lecture notes in statistics |
| spellingShingle | Barbu, Vlad Stefan Limnios, Nikolaos Semi-Markov chains and hidden semi-Markov models toward applications their use in reliability and DNA analysis Lecture notes in statistics ADN - Analyse - Modèles mathématiques Fiabilité - Modèles mathématiques Processus de Markov Mathematik Mathematisches Modell DNA Analysis Mathematics DNA Mathematical models DNA analysis Markov Chains Markov processes Models, Theoretical Reliability (Engineering) Mathematical models Reproducibility of Results Semi-Markov-Modell (DE-588)4180964-6 gnd Semi-Markov-Prozess (DE-588)4180965-8 gnd Hidden-Markov-Modell (DE-588)4352479-5 gnd |
| subject_GND | (DE-588)4180964-6 (DE-588)4180965-8 (DE-588)4352479-5 |
| title | Semi-Markov chains and hidden semi-Markov models toward applications their use in reliability and DNA analysis |
| title_auth | Semi-Markov chains and hidden semi-Markov models toward applications their use in reliability and DNA analysis |
| title_exact_search | Semi-Markov chains and hidden semi-Markov models toward applications their use in reliability and DNA analysis |
| title_full | Semi-Markov chains and hidden semi-Markov models toward applications their use in reliability and DNA analysis Vlad Stefan Barbu ; Nikolaos Limnios |
| title_fullStr | Semi-Markov chains and hidden semi-Markov models toward applications their use in reliability and DNA analysis Vlad Stefan Barbu ; Nikolaos Limnios |
| title_full_unstemmed | Semi-Markov chains and hidden semi-Markov models toward applications their use in reliability and DNA analysis Vlad Stefan Barbu ; Nikolaos Limnios |
| title_short | Semi-Markov chains and hidden semi-Markov models toward applications |
| title_sort | semi markov chains and hidden semi markov models toward applications their use in reliability and dna analysis |
| title_sub | their use in reliability and DNA analysis |
| topic | ADN - Analyse - Modèles mathématiques Fiabilité - Modèles mathématiques Processus de Markov Mathematik Mathematisches Modell DNA Analysis Mathematics DNA Mathematical models DNA analysis Markov Chains Markov processes Models, Theoretical Reliability (Engineering) Mathematical models Reproducibility of Results Semi-Markov-Modell (DE-588)4180964-6 gnd Semi-Markov-Prozess (DE-588)4180965-8 gnd Hidden-Markov-Modell (DE-588)4352479-5 gnd |
| topic_facet | ADN - Analyse - Modèles mathématiques Fiabilité - Modèles mathématiques Processus de Markov Mathematik Mathematisches Modell DNA Analysis Mathematics DNA Mathematical models DNA analysis Markov Chains Markov processes Models, Theoretical Reliability (Engineering) Mathematical models Reproducibility of Results Semi-Markov-Modell Semi-Markov-Prozess Hidden-Markov-Modell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016778218&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002447846 |
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