On the axiomatic approach to the maximum entropy principle of inference.

Abstract

Recent axiomatic derivations of the maximum entropy principle from consistency conditions are critically examined. We show that proper application of consistency conditions alone allows a wider class of functional& essentially of the form ∫dx [p(x)/g(x)]², for some real number s, to be used for inductive inference and the commonly used form - ∫dx p(x) In [p(x) / g (x)] is only a particular case. The role of the prior density g (x) is clarified. It is possible to regard it as a geometric factor, describing the coordinate system used and it does not represent information of the same kind as obtained by measurements on the system in the form of expectation values.