Much of our thinking is flawed because it is based on faulty intuition. By using the framework and tools of probability and statistics, we can overcome this to provide solutions to many real-world problems and paradoxes. We show how to do this, and find answers that are frequently very contrary to what we might expect. Along the way, we venture into diverse realms and thought experiments which challenge the way that we see the world.
- An insightful and engaging discussion of some of the key ideas of probabilistic and statistical thinking
- Many classic and novel problems, paradoxes, and puzzles
- An exploration of some of the big questions involving the use of choice and reason in an uncertain world
- The application of probability, statistics, and Bayesian methods to a wide range of subjects, including economics, finance, law, and medicine
- Exercises, references, and links for those wishing to cross-reference or to probe further
- Solutions to exercises at the end of the book
This book should serve as an invaluable and fascinating resource for university, college, and high school students who wish to extend their reading, as well as for teachers and lecturers who want to liven up their courses while retaining academic rigour. It will also appeal to anyone who wishes to develop skills with numbers or has an interest in the many statistical and other paradoxes that permeate our lives. Indeed, anyone studying the sciences, social sciences, or humanities on a formal or informal basis will enjoy and benefit from this book.
Table of Contents
1. Probability, Evidence, and Reason
2. Probability Paradoxes
3. Probability and Choice
4. Probability, Games, and Gambling
5. Probability, Truth, and Reason
6. Anomalies of Choice and Reason
7. Game Theory, Probability, and Practice
8. Further Ideas and Exercises
Solutions to Exercises
Leighton Vaughan Williams, PhD, FHEA, is Professor of Economics and Finance at Nottingham Business School, as well as Director of the Betting Research Unit and of the Political Forecasting Unit. He has researched and published extensively in the areas of probability, risk, and choice under uncertainty, and given expert witness evidence before national and international courts of law and select committees of the House of Commons and House of Lords. He has served as a senior adviser to UK Government departments, and currently teaches undergraduates and postgraduates how to apply Bayesian methods, and the tools of probability and statistics, to real-world problems and paradoxes.
"This outstanding book serves to bridge and extend the space between popular science and statistics on the one side and more formal academic learning on the other. In doing so, it is exceptional in terms of breadth, depth, rigour, clarity and accessibility. The scope and content are very well chosen and assembled, and help greatly in improving our understanding of the roles of chance, choice and reason in the world. Each section contributes a critical element of the overall jigsaw of how best to understand and investigate this world, and provides the essential toolkit required to do so. The problem sets are particularly helpful in illuminating the material. I highly recommend this book to anyone studying, or with a general interest in, the sciences or social sciences."
- Vanessa Sung, University of Southampton
"The book presents a fascinating collection of multiple problems on Bayesian techniques, probability and statistics, paradoxes and puzzles, applications to various real-world subjects, including economics, finance, law, medicine, and much more.
[. . . ] the book is full of intellectual entertainment. It is useful to instructors, educational to students of all levels, and attractive for readers interested in tools of better reasoning on any topic. The book presents a unique collection of not so widely known problems with theirmeticulous consideration by meaning and interpretation, derivation and calculation."
"This is an interesting, but curious book full of insightful, well-presented examples of how probability and Bayesian Inference can unravel initially paradoxical-sounding problems.
[. . .] The book touches on issues that are central to appropriate and rational choices in the face of uncertainty. [. . . ] A very valuable resource and one that is fun to dip into. It should find a home on many lecturers’ bookshelves."
– Series A, Royal Statistics Society