Bayes' rule with R: a tutorial introduction to Bayesian analysis
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
[Sheffield]
Sebtel Press
2016
|
| Edition: | First edition |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Literaturverzeichnis: Seite 169-172 Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | 174 Seiten Illustrationen, Diagramme |
| ISBN: | 9780993367946 0993367941 |
Staff View
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| adam_text | Contents Preface 1. An Introduction to Bayes’ Rule 1.1. 1.2. 1.3. 1.4. 1.5. Example 1: Poxy Diseases............................................... Example 2: Forkandles..................................................... Example 3: Flipping Coins ............................................ Example 4: Light Craters............................................... Forward and Inverse Probability ................................... 2. Bayes’ Rule in Pictures 2.1. 2.2. 2.3. 2.4. 2.5. 2.6. Random Variables........................................................... The Rules of Probability.................................................. Joint Probability and Coin Flips................................... Probability As Geometric Area...................................... Bayes’ Rule From Venn Diagrams.................................... Bayes’ Rule and the Medical Test ................................. 3. Discrete Parameter Values 3.1. 3.2. 3.3. 3.4. 3.5. Joint Probability Functions............................................ Patient Questions.............................................................. Deriving Bayes’ Rule ..................................................... Using Bayes’ Rule ........................................................... Bayes’ Rule and the Joint Distribution........................... 4. Continuous Parameter Values 4.1. 4.2. 4.3. 4.4. 4.5. 4.6. 4.7. 4.8. 4.9. 1 3 17 23 27 29 31 31 33 35 37 43 45 49 50 54 72 74 76 79 A Continuous Likelihood Function................................. 80 A Binomial
Prior.............................................................. 84 The Posterior.................................................................... 85 A Rational Basis For Bias............................................... 88 The Uniform Prior........................................................... 88 Finding the MAP Analytically ...................................... 93 Evolution of the Posterior............................................... 94 Reference Priors .............................................................. 99 Loss Functions.................................................................... 100
5. Gaussian Parameter Estimation 103 5.1. The Gaussian Distribution ..................................................103 5.2. Estimating the Population Mean........................................ 105 5.3. Error Bars for Gaussian Distributions ...............................110 5.4. Regression as Parameter Estimation.................................. 112 6. A Bird’s Eye View of Bayes’ Rule 117 6.1. Joint Gaussian Distributions .............................................. 117 6.2. A Bird’s-Eye View of the Joint Distribution ...................120 6.3. A Bird’s-Eye View of Bayes’ Rule........................................ 123 6.4. Slicing Through Joint Distributions..................................... 126 6.5. Statistical Independence........................................................126 7. Bayesian Wars 129 7.1. The Nature of Probability.....................................................129 7.2. Bayesian Wars ........................................................................135 7.3. A Very Short History of Bayes’ Rule.................................. 138 Further Reading 139 Appendices 141 A. Glossary 143 B. Mathematical Symbols 147 C. The Rules of Probability 151 D. Probability Density Functions 155 E. The Binomial Distribution 159 F. The Gaussian Distribution 163 G. Least-Squares Estimation 165 H. Reference Priors 167 References 169 Index 173
iscovered by an 18th century mathematician and preacher, Bayes’ rule is a cornerstone of modern probability theory. In this richly illustrated book, a range of accessible examples is used to show how Bayes’ rule is actually a natural consequence of common sense reasoning. Bayes’ rule is then derived using intuitive graphical representations of probability, and Bayesian analysis is applied to parameter estimation. The tutorial style of writing, combined with a comprehensive glossary, makes this an ideal primer for novices who wish to become familiar with the basic principles of Bayesian analysis. D Note that this book includes R (3.2) code snippets, which reproduce key numerical results and diagrams. Dr James Stone is a Reader in Vision and Computational Neuroscience at the University of Sheffield, England.
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| adam_txt |
Contents Preface 1. An Introduction to Bayes’ Rule 1.1. 1.2. 1.3. 1.4. 1.5. Example 1: Poxy Diseases. Example 2: Forkandles. Example 3: Flipping Coins . Example 4: Light Craters. Forward and Inverse Probability . 2. Bayes’ Rule in Pictures 2.1. 2.2. 2.3. 2.4. 2.5. 2.6. Random Variables. The Rules of Probability. Joint Probability and Coin Flips. Probability As Geometric Area. Bayes’ Rule From Venn Diagrams. Bayes’ Rule and the Medical Test . 3. Discrete Parameter Values 3.1. 3.2. 3.3. 3.4. 3.5. Joint Probability Functions. Patient Questions. Deriving Bayes’ Rule . Using Bayes’ Rule . Bayes’ Rule and the Joint Distribution. 4. Continuous Parameter Values 4.1. 4.2. 4.3. 4.4. 4.5. 4.6. 4.7. 4.8. 4.9. 1 3 17 23 27 29 31 31 33 35 37 43 45 49 50 54 72 74 76 79 A Continuous Likelihood Function. 80 A Binomial
Prior. 84 The Posterior. 85 A Rational Basis For Bias. 88 The Uniform Prior. 88 Finding the MAP Analytically . 93 Evolution of the Posterior. 94 Reference Priors . 99 Loss Functions. 100
5. Gaussian Parameter Estimation 103 5.1. The Gaussian Distribution .103 5.2. Estimating the Population Mean. 105 5.3. Error Bars for Gaussian Distributions .110 5.4. Regression as Parameter Estimation. 112 6. A Bird’s Eye View of Bayes’ Rule 117 6.1. Joint Gaussian Distributions . 117 6.2. A Bird’s-Eye View of the Joint Distribution .120 6.3. A Bird’s-Eye View of Bayes’ Rule. 123 6.4. Slicing Through Joint Distributions. 126 6.5. Statistical Independence.126 7. Bayesian Wars 129 7.1. The Nature of Probability.129 7.2. Bayesian Wars .135 7.3. A Very Short History of Bayes’ Rule. 138 Further Reading 139 Appendices 141 A. Glossary 143 B. Mathematical Symbols 147 C. The Rules of Probability 151 D. Probability Density Functions 155 E. The Binomial Distribution 159 F. The Gaussian Distribution 163 G. Least-Squares Estimation 165 H. Reference Priors 167 References 169 Index 173
iscovered by an 18th century mathematician and preacher, Bayes’ rule is a cornerstone of modern probability theory. In this richly illustrated book, a range of accessible examples is used to show how Bayes’ rule is actually a natural consequence of common sense reasoning. Bayes’ rule is then derived using intuitive graphical representations of probability, and Bayesian analysis is applied to parameter estimation. The tutorial style of writing, combined with a comprehensive glossary, makes this an ideal primer for novices who wish to become familiar with the basic principles of Bayesian analysis. D Note that this book includes R (3.2) code snippets, which reproduce key numerical results and diagrams. Dr James Stone is a Reader in Vision and Computational Neuroscience at the University of Sheffield, England. |
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| author | Stone, James V. |
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| edition | First edition |
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| spelling | Stone, James V. Verfasser (DE-588)1082255777 aut Bayes' rule with R a tutorial introduction to Bayesian analysis James V. Stone First edition [Sheffield] Sebtel Press 2016 174 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Literaturverzeichnis: Seite 169-172 Hier auch später erschienene, unveränderte Nachdrucke Bayes, Thomas 1702-1761 (DE-588)118657674 gnd rswk-swf Bayes-Regel (DE-588)4144221-0 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Bayes, Thomas 1702-1761 (DE-588)118657674 p Bayes-Regel (DE-588)4144221-0 s Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s DE-604 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032230247&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032230247&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Stone, James V. Bayes' rule with R a tutorial introduction to Bayesian analysis Bayes, Thomas 1702-1761 (DE-588)118657674 gnd Bayes-Regel (DE-588)4144221-0 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
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| title | Bayes' rule with R a tutorial introduction to Bayesian analysis |
| title_auth | Bayes' rule with R a tutorial introduction to Bayesian analysis |
| title_exact_search | Bayes' rule with R a tutorial introduction to Bayesian analysis |
| title_exact_search_txtP | Bayes' rule with R a tutorial introduction to Bayesian analysis |
| title_full | Bayes' rule with R a tutorial introduction to Bayesian analysis James V. Stone |
| title_fullStr | Bayes' rule with R a tutorial introduction to Bayesian analysis James V. Stone |
| title_full_unstemmed | Bayes' rule with R a tutorial introduction to Bayesian analysis James V. Stone |
| title_short | Bayes' rule with R |
| title_sort | bayes rule with r a tutorial introduction to bayesian analysis |
| title_sub | a tutorial introduction to Bayesian analysis |
| topic | Bayes, Thomas 1702-1761 (DE-588)118657674 gnd Bayes-Regel (DE-588)4144221-0 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| topic_facet | Bayes, Thomas 1702-1761 Bayes-Regel Wahrscheinlichkeitsrechnung Einführung |
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