Exponential Family Models from Bayes' Theorem under Expectation Constraints

Abstract

It is shown that a consistent application of Bayesian updating from a prior probability density to a posterior using evidence in the form of expectation constraints leads to exactly the same results as the application of the maximum entropy principle, namely a posterior belonging to the exponential family. The Bayesian updating procedure presented in this work is not expressed as a variational principle, and does not involve the concept of entropy. Therefore it conceptually constitutes a complete alternative to entropic methods of inference.