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

Format:

Book

Author/Creator:

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

Series:

Wiley series in probability and statistics.

Wiley series in probability and statistics

Language:

English

Subjects (All):

Probabilities.

Uncertainty--Mathematics.

Uncertainty.

Decision making--Mathematics.

Decision making.

Mathematical statistics.

Physical Description:

1 online resource (1 v.) : ill.

Edition:

Revised edition.

Place of Publication:

Hoboken, New Jersey : Wiley, 2014.

System Details:

text file

Summary:

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.

Contents:

Cover

Title Page

Copyright Page

Contents

Preface

Prologue

Chapter 1: Uncertainty

1.1. Introduction

1.2. Examples

1.3. Suppression of Uncertainty

1.4. The Removal of Uncertainty

1.5. The Uses of Uncertainty

1.6. The Calculus of Uncertainty

1.7. Beliefs

1.8. Decision Analysis

Chapter 2: Stylistic Questions

2.1. Reason

2.2. Unreason

2.3. Facts

2.4. Emotion

2.5. Normative and Descriptive Approaches

2.6. Simplicity

2.7. Mathematics

2.8. Writing

2.9. Mathematics Tutorial

Chapter 3: Probability

3.1. Measurement

3.2. Randomness

3.3. A Standard for Probability

3.4. Probability

3.5. Coherence

3.6. Belief

3.7. Complementary Event

3.8. Odds

3.9. Knowledge Base

3.10. Examples

3.11. Retrospect

Chapter 4: Two Events

4.1. Two Events

4.2. Conditional Probability

4.3. Independence

4.4. Association

4.5. Examples

4.6. Supposition and Fact

4.7. Seeing and Doing

Chapter 5: The Rules of Probability

5.1. Combinations of Events

5.2. Addition Rule

5.3. Multiplication Rule

5.4. The Basic Rules

5.5. Examples

5.6. Extension of the Conversation

5.7. Dutch Books

5.8. Scoring Rules

5.9. Logic Again

5.10. Decision Analysis

5.11. The Prisoners' Dilemma

5.12. The Calculus and Reality

5.13. Closure

Chapter 6: Bayes Rule

6.1. Transposed Conditionals

6.2. Learning

6.3. Bayes Rule

6.4. Medical Diagnosis

6.5. Odds Form of Bayes Rule

6.6. Forensic Evidence

6.7. Likelihood Ratio

6.8. Cromwell's Rule

6.9. A Tale of Two Urns

6.10. Ravens

6.11. Diagnosis and Related Matters

6.12. Information

Chapter 7: Measuring Uncertainty

7.1. Classical Form

7.2. Frequency Data

7.3. Exchangeability

7.4. Bernoulli Series

7.5. De Finetti's Result

7.6. Large Numbers.

7.7. Belief and Frequency

7.8. Chance

Chapter 8: Three Events

8.1. The Rules of Probability

8.2. Simpson's Paradox

8.3. Source of the Paradox

8.4. Experimentation

8.5. Randomization

8.6. Exchangeability

8.7. Spurious Association

8.8. Independence

8.9. Conclusions

Chapter 9: Variation

9.1. Variation and Uncertainty

9.2. Binomial Distribution

9.3. Expectation

9.4. Poisson Distribution

9.5. Spread

9.6. Variability as an Experimental Tool

9.7. Probability and Chance

9.8. Pictorial Representation

9.9. Probability Densities

9.10. The Normal Distribution

9.11. Variation as a Natural Phenomenon

9.12. Ellsberg's Paradox

Chapter 10: Decision Analysis

10.1. Beliefs and Actions

10.2. Comparison of Consequences

10.3. Medical Example

10.4. Maximization of Expected Utility

10.5. More on Utility

10.6. Some Complications

10.7. Reason and Emotion

10.8. Numeracy

10.9. Expected Utility

10.10. Decision Trees

10.11. The Art and Science of Decision Analysis

10.12. Further Complications

10.13. Combination of Features

10.14. Legal Applications

Chapter 11: Science

11.1. Scientific Method

11.2. Science and Education

11.3. Data Uncertainty

11.4. Theories

11.5. Uncertainty of a Theory

11.6. The Bayesian Development

11.7. Modification of Theories

11.8. Models

11.9. Hypothesis Testing

11.10. Significance Tests

11.11. Repetition

11.12. Summary

Chapter 12: Examples

12.1. Introduction

12.2. Cards

12.3. The Three Doors

12.4. The Problem of Two Daughters

12.5. Two More Daughters and Cardano

12.6. The Two Envelopes

12.7. Y2K

12.8. UFOs

12.9. Conglomerability

12.10. Efron's Dice

Chapter 13: Probability Assessment

13.1. Nonrepeatable Events

13.2. Two Events

13.3. Coherence.

13.4. Probabilistic Reasoning

13.5. Trickle Down

13.6. Summary

Chapter 14: Statistics

14.1. Bayesian Statistics

14.2. A Bayesian Example

14.3. Frequency Statistics

14.4. Significance Tests

14.5. Betting

14.6. Finance

Epilogue

Subject Index

Index of Examples

Index of Notations

EULA.

Notes:

Includes indexes.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

9781118650158

1118650158

9781118650110

1118650115

9781118650233

1118650239

OCLC:

878059685