Principles of Uncertainty (PDF)

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 assumptionJust-in-time mathematics - the presentation of ideas just before they are appliedSummary and exercises at the end of each chapterDiscussion of maximization of expected utility The basics of Markov Chain Monte Carlo computing techniquesProblems involving more than one decision-makerWritten 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.