# Principles of Uncertainty

### About the author

Joseph B. Kadane, Department of Statistics, Carnegie Mellon University, Pittsburgh, Pennsylvania, USA

**An intuitive and mathematical introduction to subjective probability and Bayesian statistics.**

An accessible, comprehensive guide to the theory of Bayesian statistics, **Principles of Uncertainty** presents the subjective Bayesian approach, which has played a pivotal role in game theory, economics, and the recent boom in Markov Chain Monte Carlo methods. Both rigorous and friendly, the book contains:

- Introductory chapters examining each new concept or assumption
- Just-in-time mathematics – the presentation of ideas just before they are applied
- Summary and exercises at the end of each chapter
- Discussion of maximization of expected utility
- The basics of Markov Chain Monte Carlo computing techniques
- Problems involving more than one decision-maker

Written in an appealing, inviting style, and packed with interesting examples, **Principles of Uncertainty** introduces the most compelling parts of mathematics, computing, and philosophy as they bear on statistics. Although many books present the computation of a variety of statistics and algorithms while barely skimming the philosophical ramifications of subjective probability, this book takes a different tack. By addressing how to think about uncertainty, this book gives readers the intuition and understanding required to choose a particular method for a particular purpose.

494 pages; ISBN 9781439861622

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Title: Principles of Uncertainty

Author: Joseph B. Kadane

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### In the press

"… it is a book about Bayesian probability, statistics, and decision making. … an excellent choice. … The exercises at the end of each chapter are well conceived and in this way most useful for checking understanding of the text. Typos and errata are rare in this book. … recommended to statisticians (without restriction of any kind), statistics students at a graduate or PhD level, and empirical researchers in general … a sound basis for a course in Bayesian probability, statistics, and decision making."

—*Biometrical Journal*, 2013

This book mainly focuses on the use of Bayesian statistics. It is written using stories and many examples to which readers can relate, and is thus an engaging and appealing text on what is generally a very dry mathematical subject.

—John J. Shea, *IEEE Electrical Insulation Magazine*, May/June 2013, Vol. 29, No. 3

This text provides a unique blend of theory, methods, philosophy and applications that is suitable for a course in Bayesian probability and statistics. … provides thought-provoking material for teaching. …

—Erkki P. Liski, *International Statistical Review*, 2012

In this remarkable book, Kadane begins at the most rudimentary level, develops all the needed mathematics on the fly, and still manages to flesh out at least the core of the whole story, slowly, thoughtfully, and rigorously, right up to graduate level. Major theorems all proved in detail appear here, but not for their own sake; the author always carefully selects them to clarify the basic meaning of the subject and his own views concerning the pitfalls and subtleties of its proper application. Summing Up: Highly recommended.

—D.V. Feldman, *CHOICE*, February 2012

**Principles of Uncertainty** is a profound and mesmerising book on the foundations and principles of subjectivist or behaviouristic Bayesian analysis. … the book is a pleasure to read. And highly recommended for teaching as it can be used at many different levels. … A must-read for sure!

—Christian Robert, The Statistics Forum/*CHANCE*, October 2011

It's a lovely book, one that I hope will be widely adopted as a course textbook.

—Michael Jordan, University of California, Berkeley, USA

A careful, complete, and lovingly written exposition of the subjective Bayesian viewpoint by one of its most eloquent and staunch defenders. Summarizes a lifetime of theory, methods, and application developments for the Bayesian inferential engine. A must-read for anyone looking for a deep understanding of the foundations of Bayesian methods and what they offer modern statistical practice.

—Bradley P. Carlin, Professor and Head of Division of Biostatistics, University of Minnesota, Minneapolis, USA