This book provides statisticians, researchers, and economists with a comprehensive guide to Bayesian probability, an analytic approach used to understand natural and social phenomena. Emerging from the author's seminal studies in the field, the book presents the ideas and principles underlying Bayesian theories, with a focus on their applications in multivariate problems where neither means nor uncertainties are known with certainty. The author highlights the advantages of Bayesian analysis over conventional frequency theory and explores the field's historical evolution, current development, and future prospects. This book is a valuable resource for practitioners seeking advanced statistical techniques to address complex problems in diverse fields, from econometrics to operations research and social science.

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Excerpt from Extended Natural Conjugate Distributions for the Multinormal Process

Furthermore, Rothenburg [4 points out an additional difficulty associated with natural conjugate analysis of the Multinormal process when this analysis is applied to reduced form systems; namely, if the joint prior of (i, E), the matrix of coefficients of the system and the inverse of the variance-covariance matrix of the residual error vector respectively, is in the natural conjugate family, then the marginal variances of all coefficients in the ith row of fl are proportional to the marginal variances of coefficients in the jth row of g. In practical problems, such a restriction is often undesirable. Zellner [5 attempts to deal with this problem.

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