Semi-Markov chains and hidden semi-Markov models toward applications: their use in reliability and DNA analysis
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
2008
|
| Series: | Lecture notes in statistics
191 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 224 S. graph. Darst. 235 mm x 155 mm |
| ISBN: | 9780387731711 0387731717 9780387731735 |
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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
|
| adam_txt |
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 |
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| index_date | 2024-07-02T22:17:14Z |
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| institution | BVB |
| isbn | 9780387731711 0387731717 9780387731735 |
| language | English |
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| physical | XIII, 224 S. graph. Darst. 235 mm x 155 mm |
| publishDate | 2008 |
| publishDateSearch | 2008 |
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| publisher | Springer |
| record_format | marc |
| series | Lecture notes in statistics |
| series2 | Lecture notes in statistics |
| spelling | Barbu, Vlad Stefan Verfasser aut Semi-Markov chains and hidden semi-Markov models toward applications their use in reliability and DNA analysis Vlad Stefan Barbu ; Nikolaos Limnios New York, NY Springer 2008 XIII, 224 S. graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Lecture notes in statistics 191 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 rswk-swf Semi-Markov-Prozess (DE-588)4180965-8 gnd rswk-swf Hidden-Markov-Modell (DE-588)4352479-5 gnd rswk-swf Semi-Markov-Prozess (DE-588)4180965-8 s DE-604 Semi-Markov-Modell (DE-588)4180964-6 s Hidden-Markov-Modell (DE-588)4352479-5 s Limnios, Nikolaos Verfasser aut Lecture notes in statistics 191 (DE-604)BV002447846 191 HBZ Datenaustausch application/pdf 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 Inhaltsverzeichnis |
| 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_exact_search_txtP | 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 |
| work_keys_str_mv | AT barbuvladstefan semimarkovchainsandhiddensemimarkovmodelstowardapplicationstheiruseinreliabilityanddnaanalysis AT limniosnikolaos semimarkovchainsandhiddensemimarkovmodelstowardapplicationstheiruseinreliabilityanddnaanalysis |