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Unification of Maximum Entropy and Bayesian Inference via Plausible Reasoning (1103.2411v4)
Published 12 Mar 2011 in cs.IT, math.IT, math.ST, physics.data-an, and stat.TH
Abstract: This paper modifies Jaynes's axioms of plausible reasoning and derives the minimum relative entropy principle, Bayes's rule, as well as maximum likelihood from first principles. The new axioms, which I call the Optimum Information Principle, is applicable whenever the decision maker is given the data and the relevant background information. These axioms provide an answer to the question "why maximize entropy when faced with incomplete information?"
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