to be published in American Statistical Association’s Business and Economics Statistics Section’s Proceedings Publication)

Bayesian analysts use a formal model, Bayes’ theorem to learn from their data in contrast to non-Bayesians who usually learn informally. In addition to proofs of Bayes ’ theorem in the literature, herein it is shown how to derive Bayes ’ theorem, the Bayesian learning model as a solution to an information theoretic optimization problem and that the solution is 100 % efficient. Since this direct link between Bayesian analysis and information theory was established in Zellner (1988), recent work has shown how this optimization approach can be employed to produce a range of optimal learning models, all of them efficient, that have been employed to solve a wide range of “non-standard ” problems, e.g., those in which likelihood functions and/or prior densities are unavailable and thus the traditional, Bayesian learning model can not be employed. These models can be compared to other available models by use of posterior odds. By having a set of optimal learning models “on the shelf ” to solve a broader range of inverse inference problems, Bayesian analysis will be even more effective than it is today. Keywords:Bayes’theorem,information theory, optimal learning models, invers