Pólya urn models:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton, FL
CRC Press
2009
|
| Schriftenreihe: | Texts in statistical science series
76 |
| Schlagworte: | |
| Online-Zugang: | Table of contents only Inhaltsverzeichnis |
| Beschreibung: | 290 S. Ill. 25 cm |
| ISBN: | 9781420059830 1420059831 |
Internformat
MARC
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| 100 | 1 | |a Mahmoud, Hosam M. |d 1954- |e Verfasser |0 (DE-588)133633160 |4 aut | |
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| 650 | 4 | |a Distribution (Probability theory) | |
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Datensatz im Suchindex
| _version_ | 1804140993994293248 |
|---|---|
| adam_text | Titel: Pólya urn models
Autor: Mahmoud, Hosam M.
Jahr: 2009
Contents
1 Urn Models and Rudiments of Discrete Probability..................1
1.1 Probability Axioms..............................................2
1.2 Random Variables...............................................3
1.3 Independence of Discrete Random Variables.....................3
1.4 Realization of Basic Discrete Distributions via Urns...............5
1.4.1 The Discrete Uniform Distribution........................6
1.4.2 The Bernoulli Distribution................................6
1.4.3 The Binomial Distribution.................................7
1.4.4 The Geometric Distribution...............................7
1.4.5 The Negative Binomial Distribution.......................8
1.4.6 The Hypergeometric Distribution.........................9
1.4.7 The Negative Hypergeometric Distribution..............10
1.4.8 The Poisson Distribution.................................10
1.4.9 The Multinomial Distributions...........................11
1.5 The Poisson Process............................................12
1.6 Markov Chains.................................................16
1.6.1 Classification of Markov Chains..........................18
1.6.2 Chapman-Kolmogorov Equations........................18
1.6.3 limit and Stationary Distributions.......................20
1.7 Exchangeability.................................................23
1.7.1 Mixtures of Distributions................................26
1.7.2 de Finetti s Theorem for Indicators.......................27
Exercises............................................................31
2 Some Classical Urn Problems.......................................35
2.1 Ballot Problems.................................................35
2.2 Occupancy Problems...........................................37
2.3 Coupon Collector s Problems...................................38
2.4 The Gambler s Ruin............................................39
2.5 Banach s Matchbox Problem....................................41
Exercises............................................................42
3 Pólya Urn Models...................................................45
3.1 Tenability.......................................................46
3.1.1 Four Negative Numbers.................................48
3.1.2 Three Negative Numbers................................48
3.1.3 Two Negative Numbers..................................48
3.1.4 One Negative Number...................................50
3.2 The Pólya-Eggenberger Urn.................................... .50
3.3 Bernard Friedman s Urn........................................54
3.4 The Bagchi-Pal urn.............................................56
3.5 The Ehrenfest Urn..............................................62
Exercises............................................................67
4 Poissonization......................................................69
4.1 The Pólya Process...............................................69
4.2 Poissonization of Multicolor Deterministic Schemes.............75
4.3 The Deterministic Monochromatic Pólya Process................76
4.4 The Pólya-Eggenberger Process.................................78
4.5 The Ehrenfest Process...........................................79
4.6 Poissonization of Schemes with Random Entries................81
Exercises............................................................85
5 The Depoissonization Heuristic.....................................87
5.1 Depoissonization of Dichromatic Pólya Processes...............91
5.2 Depoissonization of Invertible Processes........................92
5.3 Depoissonization Examples.....................................93
Exercises............................................................96
6 Urn Schemes with Random Replacement...........................99
6.1 Martingales.....................................................99
6.2 Extended Urn Schemes........................................101
6.3 Deterministic Dichromatic Extended Urn Schemes............. 102
6.3.1 Laws of Large Numbers................................102
6.3.2 Asymptotic Normality..................................108
6.4 Dichromatic Extended Urn Schemes with Random Entries ..... 112
6.5 Extended Multicolor Urn Schemes.............................114
Exercises...........................................................115
7 Analytic Urns......................................................117
7.1 Enumerating Histories in Balanced Schemes...................117
7.2 Analytic Urn Examples........................................123
7.2.1 Analytic Pólya-Eggenberger Urn........................123
7.2.2 Analytic Bernard Friedman s Urn.......................125
7.2.3 Analytic Ehrenfest Urn.................................128
7.2.4 Analytic Coupon Collector s Urn.......................130
Exercises........................................................... 133
8 Applications of Pólya Urns in Informatics.........................135
8.1 Search Trees...................................................135
8.1.1 Binary Search Trees.....................................136
8.1.2 Fringe-Balanced Trees..................................138
8.1.3 m-Ary Search Trees.....................................140
8.1.4 2-3 Trees...............................................144
8.1.5 Paged Binary Trees.....................................146
8.1.6 Bucket Quad Trees......................................148
8.1.7 Bucket k-d Trees........................................150
8.2 Recursive Trees................................................152
8.2.1 Standard Recursive Trees...............................152
8.2.2 Pyramids...............................................158
8.2.3 Plane-Oriented Recursive Trees.........................159
8.2.4 Bucket Recursive Trees..................................160
8.2.5 Sprouts.................................................162
Exercises...........................................................164
9 Urn Schemes in Bioscience.........................................167
9.1 Evolution of Species...........................................167
9.1.1 Wright-Fisher Allelic Urn Models.......................168
9.1.2 Gene Miscopying.......................................169
9.1.3 Mutation...............................................171
9.1.4 Hoppe s Urn Scheme...................................173
9.1.5 Ewens Sampling Formula..............................179
9.1.6 Phylogenetic Trees......................................184
9.2 Competitive Exclusion.........................................186
9.3 Epidemiology: Kriz Polytonomous Urn Scheme...............198
9.4 Clinical Trials..................................................200
9.4.1 Play-the-Winner Schemes...............................200
Exercises...........................................................203
10 Urns Evolving by Multiple Drawing..............................205
10.1 Urns Evolving by Drawing Pairs of Balls....................205
10.2 The Chen-Wei Urn..........................................209
10.3 Linear Rectangular Urns....................................209
10.4 Application of Rectangular Schemes in Random Circuits.....217
Exercises..........................................................220
Answers to Exercises...................................................223
Notation...............................................................267
Bibliographic Notes...................................................273
Bibliography..........................................................275
Index..................................................................283
|
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| discipline | Mathematik |
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| id | DE-604.BV035971180 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:08:49Z |
| institution | BVB |
| isbn | 9781420059830 1420059831 |
| language | English |
| lccn | 2008013347 |
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| physical | 290 S. Ill. 25 cm |
| publishDate | 2009 |
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| publishDateSort | 2009 |
| publisher | CRC Press |
| record_format | marc |
| series | Texts in statistical science series |
| series2 | Texts in statistical science series |
| spelling | Mahmoud, Hosam M. 1954- Verfasser (DE-588)133633160 aut Pólya urn models Hosam M. Mahmoud Boca Raton, FL CRC Press 2009 290 S. Ill. 25 cm txt rdacontent n rdamedia nc rdacarrier Texts in statistical science series 76 Probabilities Distribution (Probability theory) Diskrete Wahrscheinlichkeitsverteilung (DE-588)4150184-6 gnd rswk-swf Urnenmodell (DE-588)4294397-8 gnd rswk-swf Diskrete Wahrscheinlichkeitsverteilung (DE-588)4150184-6 s Urnenmodell (DE-588)4294397-8 s DE-604 Texts in statistical science series 76 (DE-604)BV022819715 76 http://www.loc.gov/catdir/toc/fy0805/2008013347.html Table of contents only HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018865188&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mahmoud, Hosam M. 1954- Pólya urn models Texts in statistical science series Probabilities Distribution (Probability theory) Diskrete Wahrscheinlichkeitsverteilung (DE-588)4150184-6 gnd Urnenmodell (DE-588)4294397-8 gnd |
| subject_GND | (DE-588)4150184-6 (DE-588)4294397-8 |
| title | Pólya urn models |
| title_auth | Pólya urn models |
| title_exact_search | Pólya urn models |
| title_full | Pólya urn models Hosam M. Mahmoud |
| title_fullStr | Pólya urn models Hosam M. Mahmoud |
| title_full_unstemmed | Pólya urn models Hosam M. Mahmoud |
| title_short | Pólya urn models |
| title_sort | polya urn models |
| topic | Probabilities Distribution (Probability theory) Diskrete Wahrscheinlichkeitsverteilung (DE-588)4150184-6 gnd Urnenmodell (DE-588)4294397-8 gnd |
| topic_facet | Probabilities Distribution (Probability theory) Diskrete Wahrscheinlichkeitsverteilung Urnenmodell |
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