This second edition of the highly acclaimed text provides a thorough account of the 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 material is accessible to readers with 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.