Weighing the odds: a course in probability and statistics
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2001
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 547 S. Illustrationen |
| ISBN: | 052180356X 052100618X |
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| 245 | 1 | 0 | |a Weighing the odds |b a course in probability and statistics |c David Williams |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2001 | |
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Record in the Search Index
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| adam_text | Contents
Preface xi
1. Introduction 1
1.1. Conditioning: an intuitive first look 1
1.2. Sharpening our intuition 18
1.3. Probability as Pure Maths 23
1.4. Probability as Applied Maths 25
1.5. First remarks on Statistics 26
1.6. Use of Computers 31
2. Events and Probabilities 35
2.1. Possible outcome w, actual outcome wact; and Events 36
2.2. Probabilities 39
2.3. Probability and Measure 42
3. Random Variables, Means and Variances 47
3.1. Random Variables 47
3.2. DFs, pmfs and pdfs 50
3.3. Means in the case when U is finite 56
3.4. Means in general 59
3.5. Variances and Covariances 65
vii
viii
4. Conditioning and Independence 73
4.1. Conditional probabilities 73
4.2. Independence 96
4.3. Laws of large numbers 103
4.4. Random Walks: a first look 116
4.5. A simple strong Markov principle 127
4.6. Simulation of IID sequences 130
5. Generating Functions; and the Central Limit Theorem 141
5.1. General comments on the
use of Generating Functions (GFs) 142
5.2. Probability generating functions (pgfs) 143
5.3. Moment Generating Functions (MGFs) 146
5.4. The Central Limit Theorem (CLT) 156
5.5. Characteristic Functions (CFs) 166
6. Confidence Intervals for one parameter models 169
6.1. Introduction 169
6.2. Some commonsense Frequentist CIs 173
6.3. Likelihood; sufficiency; exponential family 181
6.4. Brief notes on Point Estimation 187
6.5. Maximum Likelihood Estimators (MLEs) and associated CIs . . . 192
6.6. Bayesian Confidence Intervals 199
6.7. Hypothesis Testing if you must 222
ix
7. Conditional pdfs and multi parameter Bayesian Statistics 240
7.1. Joint and conditional pmfs 240
7.2. Jacobians 243
7.3. Joint pdfs; transformations 246
7.4. Conditional pdfs 258
7.5. Multi parameter Bayesian Statistics 265
8. Linear Models, ANOVA, etc 283
8.1. Overview and motivation 283
8.2. The Orthonormality Principle and the F test 295
8.3. Five basic models: the Mathematics 304
8.4. Goodness of fit; robustness; hierarchical models 339
8.5. Multivariate Normal (MVN) Distributions 365
9. Some further Probability 383
9.1. Conditional Expectation 385
9.2. Martingales 406
9.3. Poisson Processes (PPs) 426
10. Quantum Probability and Quantum Computing 440
10.1. Quantum Computing: a first look 441
10.2. Foundations of Quantum Probability 448
10.3. Quantum computing: a closer look 463
10.4. Spin and Entanglement 472
10.5. Spin and the Dirac equation 485
10.6. Epilogue 491
X
Appendix A. Some Prerequisites and Addenda 495
Appendix Al. O notation 495
Appendix A2. Results of Taylor type 495
Appendix A3. o notation 496
Appendix A4. Countable and uncountable sets 496
Appendix A5. The Axiom of Choice 498
Appendix A6. A non Borel subset of [0,1] 499
Appendix A7. Static variables in C 499
Appendix A8. A non uniqueness example for moments 500
Appendix A9. Proof of a Two Envelopes result 500
Appendix B. Discussion of some Selected Exercises 502
Appendix C. Tables 514
Table of the normal distribution function 515
Upper percentage points for t 516
Upper percentage points for x2 517
Upper 5% percentage points for F 518
Appendix D. A small Sample of the Literature 519
Bibliography 525
Index 539
|
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| isbn | 052180356X 052100618X |
| language | English |
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| physical | XVII, 547 S. Illustrationen |
| publishDate | 2001 |
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| spelling | Williams, David 1938- Verfasser (DE-588)139651608 aut Weighing the odds a course in probability and statistics David Williams 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2001 XVII, 547 S. Illustrationen txt rdacontent n rdamedia nc rdacarrier Statistik Probabilities Statistics Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s DE-604 Statistik (DE-588)4056995-0 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009526129&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Williams, David 1938- Weighing the odds a course in probability and statistics Statistik Probabilities Statistics Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4064324-4 (DE-588)4056995-0 (DE-588)4123623-3 |
| title | Weighing the odds a course in probability and statistics |
| title_auth | Weighing the odds a course in probability and statistics |
| title_exact_search | Weighing the odds a course in probability and statistics |
| title_full | Weighing the odds a course in probability and statistics David Williams |
| title_fullStr | Weighing the odds a course in probability and statistics David Williams |
| title_full_unstemmed | Weighing the odds a course in probability and statistics David Williams |
| title_short | Weighing the odds |
| title_sort | weighing the odds a course in probability and statistics |
| title_sub | a course in probability and statistics |
| topic | Statistik Probabilities Statistics Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Statistik Probabilities Statistics Wahrscheinlichkeitsrechnung Lehrbuch |
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