Understanding uncertainty / Dennis V. Lindley, Minehead, Somerset, England.

Format:

Book

Author/Creator:

Lindley, D. V. (Dennis Victor), 1923-2013, author.

Series:

Wiley series in probability and statistics

Language:

English

Subjects (All):

Probabilities.

Uncertainty--Mathematics.

Uncertainty.

Decision making--Mathematics.

Decision making.

Mathematical statistics.

Mathematics.

Genre:

Electronic books.

Physical Description:

1 online resource (422 pages).

Edition:

Revised edition.

Place of Publication:

Hoboken, New Jersey : Wiley, 2014.

System Details:

text file

Summary:

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. Book jacket.

Contents:

Chapter 1 Uncertainty 1

1.1 Introduction 1

1.2 Examples 2

1.3 Suppression of Uncertainty 11

1.4 The Removal of Uncertainty 13

1.5 The Uses of Uncertainty 15

1.6 The Calculus of Uncertainty 17

1.7 Beliefs 18

1.8 Decision Analysis 20

Chapter 2 Stylistic Questions 23

2.1 Reason 23

2.2 Unreason 26

2.3 Facts 28

2.4 Emotion 29

2.5 Normative and Descriptive Approaches 31

2.6 Simplicity 33

2.7 Mathematics 35

2.8 Writing 37

2.9 Mathematics Tutorial 38

Chapter 3 Probability 45

3.1 Measurement 45

3.2 Randomness 48

3.3 A Standard for Probability 50

3.4 Probability 52

3.5 Coherence 54

3.6 Belief 56

3.7 Complementary Event 58

3.8 Odds 60

3.9 Knowledge Base 63

3.10 Examples 66

3.11 Retrospect 68

Chapter 4 Two Events 69

4.1 Two Events 69

4.2 Conditional Probability 72

4.3 Independence 75

4.4 Association 77

4.5 Examples 79

4.6 Supposition and Fact 81

4.7 Seeing and Doing 82

Chapter 5 The Rules of Probability 85

5.1 Combinations of Events 85

5.2 Addition Rule 87

5.3 Multiplication Rule 89

5.4 The Basic Rules 92

5.5 Examples 95

5.6 Extension of the Conversation 98

5.7 Dutch Books 101

5.8 Scoring Rules 103

5.9 Logic Again 105

5.10 Decision Analysis 106

5.11 The Prisoners' Dilemma 107

5.12 The Calculus and Reality 110

5.13 Closure 112

Chapter 6 Bayes Rule 113

6.1 Transposed Conditionals 113

6.2 Learning 116

6.3 Bayes Rule 118

6.4 Medical Diagnosis 119

6.5 Odds Form of Bayes Rule 123

6.6 Forensic Evidence 125

6.7 Likelihood Ratio 127

6.8 Cromwell's Rule 129

6.9 A Tale of Two Urns 131

6.10 Ravens 135

6.11 Diagnosis and Related Matters 138

6.12 Information 140

Chapter 7 Measuring Uncertainty 143

7.1 Classical Form 143

7.2 Frequency Data 145

7.3 Exchangeability 147

7.4 Bernoulli Series 151

7.5 De Finetti's Result 152

7.6 Large Numbers 154

7.7 Belief and Frequency 157

7.8 Chance 161

Chapter 8 Three Events 165

8.1 The Rules of Probability 165

8.2 Simpson's Paradox 168

8.3 Source of the Paradox 170

8.4 Experimentation 171

8.5 Randomization 173

8.6 Exchangeability 176

8.7 Spurious Association 181

8.8 Independence 183

8.9 Conclusions 186

Chapter 9 Variation 189

9.1 Variation and Uncertainty 189

9.2 Binomial Distribution 191

9.3 Expectation 195

9.4 Poisson Distribution 197

9.5 Spread 201

9.6 Variability as an Experimental Tool 204

9.7 Probability and Chance 206

9.8 Pictorial Representation 208

9.9 Probability Densities 212

9.10 The Normal Distribution 213

9.11 Variation as a Natural Phenomenon 217

9.12 Ellsberg's Paradox 219

Chapter 10 Decision Analysis 225

10.1 Beliefs and Actions 225

10.2 Comparison of Consequences 227

10.3 Medical Example 231

10.4 Maximization of Expected Utility 234

10.5 More on Utility 236

10.6 Some Complications 238

10.7 Reason and Emotion 240

10.8 Numeracy 242

10.9 Expected Utility 245

10.10 Decision Trees 246

10.11 The Art and Science of Decision Analysis 249

10.12 Further Complications 252

10.13 Combination of Features 256

10.14 Legal Applications 260

Chapter 11 Science 265

11.1 Scientific Method 265

11.2 Science and Education 266

11.3 Data Uncertainty 268

11.4 Theories 271

11.5 Uncertainty of a Theory 276

11.6 The Bayesian Development 278

11.7 Modification of Theories 281

11.8 Models 284

11.9 Hypothesis Testing 287

11.10 Significance Tests 291

11.11 Repetition 293

11.12 Summary 296

Chapter 12 Examples 299

12.1 Introduction 299

12.2 Cards 300

12.3 The Three Doors 301

12.4 The Problem of Two Daughters 305

12.5 Two More Daughters and Cardano 309

12.6 The Two Envelopes 313

12.7 Y2K 316

12.8 UFOs 317

12.9 Conglomerability 321

12.10 Efron's Dice 323

Chapter 13 Probability Assessment 327

13.1 Nonrepeatable Events 327

13.2 Two Events 329

13.3 Coherence 333

13.4 Probabilistic Reasoning 336

13.5 Trickle Down 337

13.6 Summary 341

Chapter 14 Statistics 343

14.1 Bayesian Statistics 343

14.2 A Bayesian Example 346

14.3 Frequency Statistics 350

14.4 Significance Tests 355

14.5 Betting 360

14.6 Finance 365.

Notes:

Includes indexes.

Description based on print version record.

Local Notes:

Electronic reproduction. Palo Alto, Calif. : ebrary, 2014. Available via World Wide Web. Access may be limited to ebrary affiliated libraries.

Other Format:

Print version: Lindley, Dennis V (Dennis Victor), 1923- Understanding uncertainty.

ISBN:

9781118650110

Access Restriction:

Restricted for use by site license.