## Bayesian TheoryThis highly acclaimed text, now available in paperback, provides a thorough account of key 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 of the theory, which provides, in particular, a detailed discussion of the problem of specification of so-called prior ignorance . The work is written from the authors s committed Bayesian perspective, but an overview of non-Bayesian theories is also provided, and each chapter contains a wide-ranging critical re-examination of controversial issues. The level of mathematics used is such that most 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. 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 |

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A. F. M. Smith Amer approach approximation Assoc Axiom Bayes estimate Bayes factors Bayesian analysis Bayesian inference Bayesian Statistics conditional conﬁdence conjugate prior consequences consider context corresponding D. V. Lindley decision problem decision theory deﬁned Deﬁnition degrees of belief denote discussion estimation example exchangeable sequence expected utility exponential family Finetti ﬁnite ﬁrst ﬁxed follows framework frequentist generalised given hypothesis identiﬁed J. M. Bernardo judgements Kadane Laplace approximation likelihood Lindley and A. F. M. linear M. H. DeGroot mathematical maximises multivariate normal North-Holland nuisance parameters observed optimal options parametric model posterior distribution predictive prior distribution probability distributions probability measure procedure Proposition quantitative coherence random quantities reference posterior reference prior representation result score function Section signiﬁcance speciﬁcation Statistical Inference Statistics 4 J. M. structure sufﬁcient statistic theorem typically uncertainty University Press utility function vector Wiley Zellner