Principles of Uncertainty

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.