Weighing the Odds
A Course in Probability and Statistics

An advanced textbook; with many examples and exercises, often with hints or solutions; code is provided for computational examples and simulations.

David Williams (Author)

9780521006187, Cambridge University Press

Paperback, published 2 August 2001

568 pages, 35 tables 225 exercises
24.7 x 17.6 x 3 cm, 1.13 kg

'… the book?s unusual approach and entertaining style results in an introduction to statistics which is unusually accessible to an applied mathematics audience … a very readable book, from which I learned a great deal and into which I have been continuously dipping since I finished it. I would recommend it to anyone, from final year undergraduate, to an established researcher in nonlinear science. They might be surprised how interesting statistics can be, and perhaps respond more positively next time they are asked to fit data to a model.' Nonlinear Science News

Statistics do not lie, nor is probability paradoxical. You just have to have the right intuition. In this lively look at both subjects, David Williams convinces mathematics students of the intrinsic interest of statistics and probability, and statistics students that the language of mathematics can bring real insight and clarity to their subject. He helps students build the intuition needed, in a presentation enriched with examples drawn from all manner of applications, e.g., genetics, filtering, the Black–Scholes option-pricing formula, quantum probability and computing, and classical and modern statistical models. Statistics chapters present both the Frequentist and Bayesian approaches, emphasising Confidence Intervals rather than Hypothesis Test, and include Gibbs-sampling techniques for the practical implementation of Bayesian methods. A central chapter gives the theory of Linear Regression and ANOVA, and explains how MCMC methods allow greater flexibility in modelling. C or WinBUGS code is provided for computational examples and simulations. Many exercises are included; hints or solutions are often provided.

Preface
1. Introduction
2. Events and probabilities
3. Random variables, means and variances
4. Conditioning and independence
5. Generating functions and the central limit theorem
6. Confidence intervals for 1-parameter models
7. Conditional pdfs and multi-parameter Bayesian statistics
8. Linear models, ANOVA etc
9. Some further probability
10. Quantum probability and quantum computing
Appendix A. Some prerequisites and addenda
Appendix B. Discussion of some selected exercises
Appendix C. Tables
Appendix D. A small sample of the literature
Bibliography
Index.

Subject Areas: Probability & statistics [PBT], Calculus & mathematical analysis [PBK]