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- W2155969596 abstract "An attempt is made to determine the logically consistent rules for selecting a vector from any feasible set defined by linear constraints, when either all $n$-vectors or those with positive components or the probability vectors are permissible. Some basic postulates are satisfied if and only if the selection rule is to minimize a certain function which, if a prior guess is available, is a measure of distance from the prior guess. Two further natural postulates restrict the permissible distances to the author's $f$-divergences and Bregman's divergences, respectively. As corollaries, axiomatic characterizations of the methods of least squares and minimum discrimination information are arrived at. Alternatively, the latter are also characterized by a postulate of composition consistency. As a special case, a derivation of the method of maximum entropy from a small set of natural axioms is obtained." @default.
- W2155969596 created "2016-06-24" @default.
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- W2155969596 date "1991-12-01" @default.
- W2155969596 modified "2023-10-15" @default.
- W2155969596 title "Why Least Squares and Maximum Entropy? An Axiomatic Approach to Inference for Linear Inverse Problems" @default.
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- W2155969596 doi "https://doi.org/10.1214/aos/1176348385" @default.
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