Editing Principle of maximum entropy (section)

==Overview==
In most practical cases, the stated prior data or testable information is given by a set of [[conserved quantities]] (average values of some moment functions), associated with the [[probability distribution]] in question. This is the way the maximum entropy principle is most often used in [[statistical thermodynamics]]. Another possibility is to prescribe some [[symmetries]] of the probability distribution. The equivalence between [[conserved quantities]] and corresponding [[symmetry group]]s implies a similar equivalence for these two ways of specifying the testable information in the maximum entropy method.

The maximum entropy principle is also needed to guarantee the uniqueness and consistency of probability assignments obtained by different methods, [[statistical mechanics]] and [[logical inference]] in particular.

The maximum entropy principle makes explicit our freedom in using different forms of [[Prior probability|prior data]]. As a special case, a uniform [[prior probability]] density (Laplace's [[principle of indifference]], sometimes called the principle of insufficient reason), may be adopted. Thus, the maximum entropy principle is not merely an alternative way to view the usual methods of inference of classical statistics, but represents a significant conceptual generalization of those methods.

However these statements do not imply that thermodynamical systems need not be shown to be [[ergodic]] to justify treatment as a [[statistical ensemble]].

In ordinary language, the principle of maximum entropy can be said to express a claim of epistemic modesty, or of maximum ignorance. The selected distribution is the one that makes the least claim to being informed beyond the stated prior data, that is to say the one that admits the most ignorance beyond the stated prior data.