The Poisson-Dirichlet distribution and related topics: models and asymptotic behaviors
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2010
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| Schriftenreihe: | Probability and its applications
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| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XIII, 218 S. |
| ISBN: | 9783642111938 |
Internformat
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Datensatz im Suchindex
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| adam_text |
CONTENTS PARTI MODELS 1 INTRODUCTION 3 1.1 DISCRETE MODELS 3 1.1.1
GENETIC BACKGROUND 3 1.1.2 THE WRIGHT-FISHER MODEL 5 1.1.3 THE MORAN
MODEL 7 1.2 DIFFUSION APPROXIMATION 8 1.3 AN IMPORTANT RELATION 11 1.4
NOTES 13 2 THE POISSON-DIRICHLET DISTRIBUTION 15 2. 1 DEFINITION AND
POISSON PROCESS REPRESENTATION 15 2.2 PERMAN'S FORMULA 17 2.3 MARGINAL
DISTRIBUTION 22 2.4 SIZE-BIASED SAMPLING AND THE GEM REPRESENTATION 24
2.5 THE EWENS SAMPLING FORMULA 26 2.6 SCALE-INVARIANT POISSON PROCESS 33
2.7 URN-BASED MODELS 36 2.7.1 HOPPE'S URN 36 2.7.2 LINEAR BIRTH PROCESS
WITH IMMIGRATION 38 2.7.3 A MODEL OF JOYCE AND TAVARE 44 2.8 THE
DIRICHLET PROCESS 46 2.9 NOTES 51 3 THE TWO-PARAMETER POISSON-DIRICHLET
DISTRIBUTION 53 3.1 DEFINITION 53 3.2 MARGINAL DISTRIBUTIONS 54 3.3 THE
PITMAN SAMPLING FORMULA 58 3.4 URN-TYPE CONSTRUCTION 62 3.5 NOTES 66
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1000035816 DIGITALISIERT
DURCH XII CONTENTS 4 THE COALESCENT 67 4.1 KINGMAN'S N-COALESCENT 67 4.2
THE COALESCENT 72 4.3 THE PURE-DEATH MARKOV CHAIN 73 4.4 NOTES 80 5
STOCHASTIC DYNAMICS 81 5.1 INFINITELY-MANY-NEUTRAL-ALLELES MODEL 81 5.2
A FLEMING-VIOT PROCESS 85 5.3 THE STRUCTURE OF TRANSITION FUNCTIONS 93
5.4 A MEASURE-VALUED BRANCHING DIFFUSION WITH IMMIGRATION 107 5.5
TWO-PARAMETER GENERALIZATIONS 109 5.6 NOTES ILL 6 PARTICLE
REPRESENTATION 113 6.1 EXCHANGEABILITY AND RANDOM PROBABILITY MEASURES
113 6.2 THE MORAN PROCESS AND THE FLEMING-VIOT PROCESS 116 6.3 THE
DONNELLY-KURTZ LOOK-DOWN PROCESS 120 6.4 EMBEDDED COALESCENT 123 6.5
NOTES 124 PART II ASYMPTOTIC BEHAVIORS 7 FLUCTUATION THEOREMS 127 7.1
THE POISSON-DIRICHLET DISTRIBUTION 127 7.2 THE DIRICHLET PROCESS 134 7.3
GAUSSIAN LIMITS 142 7.4 NOTES 150 8 LARGE DEVIATIONS FOR THE
POISSON-DIRICHLET DISTRIBUTION 151 8.1 LARGE MUTATION RATE 151 8.1.1 THE
POISSON-DIRICHLET DISTRIBUTION 151 8.1.2 THE TWO-PARAMETER
POISSON-DIRICHLET DISTRIBUTION 158 8.2 SMALL MUTATION RATE 160 8.2.1 THE
POISSON-DIRICHLET DISTRIBUTION 160 8.2.2 TWO-PARAMETER GENERALIZATION
168 8.3 APPLICATIONS 171 8.4 NOTES 178 9 CONTENTS XIUE A POISSON PROCESS
AND POISSON RANDOM MEASURE 199 A.I DEFINITIONS 199 A.2 PROPERTIES 200 B
BASICS OF LARGE DEVIATIONS 203 REFERENCES 209 INDEX 217 |
| any_adam_object | 1 |
| author | Feng, Shui 1962- |
| author_GND | (DE-588)141696036 |
| author_facet | Feng, Shui 1962- |
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| dewey-full | 519.233 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.233 |
| dewey-search | 519.233 |
| dewey-sort | 3519.233 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-20T10:34:56Z |
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| isbn | 9783642111938 |
| language | English |
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| physical | XIII, 218 S. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer |
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| series2 | Probability and its applications |
| spelling | Feng, Shui 1962- Verfasser (DE-588)141696036 aut The Poisson-Dirichlet distribution and related topics models and asymptotic behaviors Shui Feng Berlin [u.a.] Springer 2010 XIII, 218 S. txt rdacontent n rdamedia nc rdacarrier Probability and its applications Poisson-Prozess (DE-588)4174971-6 gnd rswk-swf Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd rswk-swf Wahrscheinlichkeitsverteilung (DE-588)4121894-2 s Poisson-Prozess (DE-588)4174971-6 s DE-604 Erscheint auch als Online-Ausgabe 978-3-642-11194-5 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3423985&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020198962&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Feng, Shui 1962- The Poisson-Dirichlet distribution and related topics models and asymptotic behaviors Poisson-Prozess (DE-588)4174971-6 gnd Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd |
| subject_GND | (DE-588)4174971-6 (DE-588)4121894-2 |
| title | The Poisson-Dirichlet distribution and related topics models and asymptotic behaviors |
| title_auth | The Poisson-Dirichlet distribution and related topics models and asymptotic behaviors |
| title_exact_search | The Poisson-Dirichlet distribution and related topics models and asymptotic behaviors |
| title_full | The Poisson-Dirichlet distribution and related topics models and asymptotic behaviors Shui Feng |
| title_fullStr | The Poisson-Dirichlet distribution and related topics models and asymptotic behaviors Shui Feng |
| title_full_unstemmed | The Poisson-Dirichlet distribution and related topics models and asymptotic behaviors Shui Feng |
| title_short | The Poisson-Dirichlet distribution and related topics |
| title_sort | the poisson dirichlet distribution and related topics models and asymptotic behaviors |
| title_sub | models and asymptotic behaviors |
| topic | Poisson-Prozess (DE-588)4174971-6 gnd Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd |
| topic_facet | Poisson-Prozess Wahrscheinlichkeitsverteilung |
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