This two volume set is a collection of 30 classic papers presenting ideas which have now become standard in the field of Bayesian inference. Topics covered include the central field of statistical inference as well as applications to areas of probability theory, information theory, utility theory and computational theory. It is organized into seven sections: foundations, information theory and prior distributions; robustness and outliers; hierarchical, multivariate and non-parametric models; asymptotics; computations and Monte Carlo methods; and Bayesian econometrics.