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Bayesian Theory is the first volume of a related series of three and will be followed by Bayesian Computation, and Bayesian Methods. The series aims to provide an up-to-date overview of the why?, how? and what? of Bayesian statistics. This volume provides a thorough account of key basic concepts and theoretical results, with particular emphasis on viewing statistical inference as a special case of decision theory. Information-theoretic concepts play a central role in the development, which provides, in particular, a detailed treatment of the problem of specification of so-called "prior ignorance". The work is written from the authors' committed Bayesian perspective, but an overview of non-Bayesian theories is provided, and each chapter contains a wide-ranging critical re-examination of controversial issues. The level of mathematics used is such that most material should be accessible to readers with a knowledge of advanced calculus. In particular, no knowledge of abstract measure theory is assumed, and the emphasis throughout is on statistical concepts rather than rigorous mathematics. The book will be an ideal source for all students and researchers in statistics, mathematics, decision analysis, economic and business studies, and all branches of science and engineering, who wish to further their understanding of Bayesian statistics.