Understanding uncertainty
著者
書誌事項
Understanding uncertainty
(Wiley series in probability and mathematical statistics)
Wiley, c2014
Rev. ed
- : cloth
大学図書館所蔵 全16件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Includes bibliographical references and indexes
内容説明・目次
内容説明
Praise for the First Edition "...a reference for everyone who is interested in knowing and handling uncertainty."
-Journal of Applied Statistics
The critically acclaimed First Edition of Understanding Uncertainty provided a study of uncertainty addressed to scholars in all fields, showing that uncertainty could be measured by probability, and that probability obeyed three basic rules that enabled uncertainty to be handled sensibly in everyday life. These ideas were extended to embrace the scientific method and to show how decisions, containing an uncertain element, could be rationally made.
Featuring new material, the Revised Edition remains the go-to guide for uncertainty and decision making, providing further applications at an accessible level including:
A critical study of transitivity, a basic concept in probability
A discussion of how the failure of the financial sector to use the proper approach to uncertainty may have contributed to the recent recession
A consideration of betting, showing that a bookmaker's odds are not expressions of probability
Applications of the book's thesis to statistics
A demonstration that some techniques currently popular in statistics, like significance tests, may be unsound, even seriously misleading, because they violate the rules of probability
Understanding Uncertainty, Revised Edition is ideal for students studying probability or statistics and for anyone interested in one of the most fascinating and vibrant fields of study in contemporary science and mathematics.
目次
Preface xi
Prologue xiii
1. Uncertainty 1
1.1. Introduction 1
1.2. Examples 2
1.3. Suppression of Uncertainty 7
1.4. The Removal of Uncertainty 8
1.5. The Uses of Uncertainty 9
1.6. The Calculus of Uncertainty 11
1.7. Beliefs 12
1.8. Decision Analysis 13
2. Stylistic Questions 15
2.1. Reason 15
2.2. Unreason 17
Literature 17
Advertising 17
Politics 18
Law 18
Television 18
2.3. Facts 19
2.4. Emotion 19
2.5. Prescriptive and Descriptive Approaches 20
2.6. Simplicity 22
2.7. Mathematics 23
2.8. Writing 25
2.9. Mathematics Tutorial 26
3. Probability 30
3.1. Measurement 30
3.2. Randomness 32
3.3. A Standard for Probability 34
3.4. Probability 35
3.5. Coherence 36
3.6. Belief 37
3.7. Complementary Event 39
3.8. Odds 40
3.9. Knowledge Base 43
3.10. Examples 44
3.11. Retrospect 46
4. Two Events 47
4.1. Two Events 47
4.2. Conditional Probability 49
4.3. Independence 51
4.4. Association 53
4.5. Examples 54
4.6. Supposition and Fact 56
4.7. Seeing and Doing 57
5. The Rules of Probability 59
5.1. Combinations of Events 59
5.2. Addition Rule 61
5.3. Multiplication Rule 62
5.4. The Basic Rules 64
5.5. Examples 66
5.6. Extension of the Conversation 68
5.7. Dutch Books 70
5.8. Scoring Rules 72
5.9. Logic Again 73
5.10. Decision Analysis 74
5.11. The Prisoners' Dilemma 75
5.12. The Calculus and Reality 76
6. Bayes Rule 79
6.1. Transposed Conditionals 79
6.2. Learning 81
6.3. Bayes Rule 82
6.4. Medical Diagnosis 83
6.5. Odds Form of Bayes Rule 86
6.6. Forensic Evidence 88
6.7. Likelihood Ratio 89
6.8. Cromwell's Rule 90
6.9. A Tale of Two Urns 92
6.10. Ravens 94
6.11. Diagnosis and Related Matters 97
6.12. Information 98
7. Measuring Uncertainty 101
7.1. Classical Form 101
7.2. Frequency Data 103
7.3. Exchangeability 104
7.4. Bernoulli Series 106
7.5. De Finetti's Result 107
7.6. Large Numbers 109
7.7. Belief and Frequency 111
7.8. Chance 114
8. Three Events 117
8.1. The Rules of Probability 117
8.2. Simpson's Paradox 119
8.3. Source of the Paradox 121
8.4. Experimentation 122
8.5. Randomization 123
8.6. Exchangeability 125
8.7. Spurious Association 128
8.8. Independence 130
8.9. Conclusions 132
9. Variation 134
9.1. Variation and Uncertainty 134
9.2. Binomial Distribution 135
9.3. Expectation 137
9.4. Poisson Distribution 139
9.5. Spread 142
9.6. Variability as an Experimental Tool 144
9.7. Probability and Chance 145
9.8. Pictorial Representation 147
9.9. The Normal Distribution 150
9.10. Variation as a Natural Phenomenon 152
9.11. Ellsberg's Paradox 154
10. Decision Analysis 158 10.1. Beliefs and Actions 158
10.2. Comparison of Consequences 160
10.3. Medical Example 162
10.4. Maximization of Expected Utility 164
10.5. More on Utility 165
10.6. Some Complications 167
10.7. Reason and Emotion 168
10.8. Numeracy 170
10.9. Expected Utility 171
10.10. Decision Trees 172
10.11. The Art and Science of Decision Analysis 175
10.12. Further Complications 177
10.13. Combination of Features 179
10.14. Legal Applications 182
11. Science 186
11.1. Scientific Method 186
11.2. Science and Education 187
11.3. Data Uncertainty 188
11.4. Theories 190
11.5. Uncertainty of a Theory 193
11.6. The Bayesian Development 195
11.7. Modification of Theories 197
11.8. Models 199
11.9. Hypothesis Testing 202
11.10. Significance Tests 204
11.11. Repetition 206
11.12. Summary 208
12. Examples 211
12.1. Introduction 211
12.2. Cards 212
12.3. The Three Doors 213
12.4. The Newcomers to Your Street 215
12.5. The Two Envelopes 217
12.6. Y2K 220
12.7. UFOs 221
12.8. Conglomerability 224
13. Probability Assessment 226
13.1. Nonrepeatable Events 226
13.2. Two Events 227
13.3. Coherence 230
13.4. Probabilistic Reasoning 233
13.5. Trickle Down 234
13.6. Summary 236
Epilogue 238
Subject Index 243
Index of Examples 248
Index of Notations 250
「Nielsen BookData」 より