Editing Principle of maximum entropy (section)

==Testable information==
The principle of maximum entropy is useful explicitly only when applied to ''testable information''. Testable information is a statement about a probability distribution whose truth or falsity is well-defined. For example, the statements

:the [[expected value|expectation]] of the variable <math>x</math> is 2.87
and
:<math>p_2 + p_3 > 0.6</math>

(where <math>p_2</math> and <math>p_3</math> are probabilities of events) are statements of testable information.

Given testable information, the maximum entropy procedure consists of seeking the [[probability distribution]] which maximizes [[information entropy]], subject to the constraints of the information. This constrained optimization problem is typically solved using the method of [[Lagrange multiplier]]s.<ref>{{Cite book |last1=Sivia |first1=Devinderjit |url=https://books.google.com/books?id=Kxx8CwAAQBAJ&dq=data+analysis+a+bayesian+tutorial&pg=PR9 |title=Data Analysis: A Bayesian Tutorial |last2=Skilling |first2=John |date=2006-06-02 |publisher=OUP Oxford |isbn=978-0-19-154670-9 |language=en}}</ref>

Entropy maximization with no testable information respects the universal "constraint" that the sum of the probabilities is one. Under this constraint, the maximum entropy discrete probability distribution is the [[uniform distribution (discrete)|uniform distribution]],

:<math>p_i=\frac{1}{n}\ {\rm for\ all}\ i\in\{\,1,\dots,n\,\}.</math>