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Is Maximum Entropy rule equivalent to non-informativeness?

In other words, when maximizing the entropy of a distribution, given some known stuff, is it equivalent to finding to most non-informative distributions? If so, how do you justify this mathematically?

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  • $\begingroup$ It is as non-informative as it can mathematically be, given constraints on ignorance imposed by information. I've found John Harte's explanation in "Maximum Entropy and Ecology" to be quite accessible. $\endgroup$ Aug 16 '13 at 5:27
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    $\begingroup$ This will sound pedantic, but maximum entropy distributions are non-informative whenever you interpret entropy as "a lack of information". In many situations this interpretation makes sense, but interpretations lie outside the scope of what can be justified with mathematics. $\endgroup$
    – caburke
    Aug 16 '13 at 6:55
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    $\begingroup$ +1. For example, many people talk informally about (say) extracting the information from the data, and this often is a matter of what is scientifically or practically interesting or important and scientists and practitioners often have a good sense of that. But it is crucial here that "information" is not defined, and there are many contexts in which defining it precisely would rid us of a useful word. We could always find another word, but "informative" will not always mean "in an information theory sense" in statistical discussions. $\endgroup$
    – Nick Cox
    Aug 16 '13 at 7:53
  • $\begingroup$ Yeah, all of this make sense, but I am looking for something more formal. May be asking for too much .... $\endgroup$
    – Daniel
    Aug 16 '13 at 13:29
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My understanding is that these are two ways of stating the same thing. So it's a tautology or a question of alternative terminology.

E.T. Jaynes's book is widely considered canonical. http://ksvanhorn.com/bayes/jaynes/ is a kind of back door start to the book and commentary.

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The Maximum Entropy Rule is a conditioning rule for least bias in the case where the sought after distribution is under-determined. As such it gives the largest possible probability weighting to competing hypotheses given the stated constraints.

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