Updating Probabilities

Abstract

We show that Skilling's method of induction leads to a unique general theory of inductive inference, the method of Maximum relative Entropy (ME). The main tool for updating probabilities is the logarithmic relative entropy; other entropies such as those of Renyi or Tsallis are ruled out. We also show that Bayes updating is a special case of ME updating and thus, that the two are completely compatible.Comment: Presented at MaxEnt 2006, the 26th International Workshop on Bayesian Inference and Maximum Entropy Methods (July 8-13, 2006, Paris, France