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- W1597376089 abstract "Consider the problem of estimating a probability distribution given only partial information on the distribution. When the partial information is based on a random sample drawn from a population following the unknown distribution, a Bayesian construction might provide the mode of the posterior distribution as a best estimate. However, when the partial information consists instead of deterministic constraints on the known distribution, it seems that no one best estimate can be singled out from the set of distributions consistent with the information. However, Jaynes [] in 1956 introduced a principle of maximum entropy, in which he proposed choosing a probability distribution of maximum entropy H(q)among those consistent with the constraints. He justified this choice [] with a correspondence principle demonstrating that if the generating distribution were the uniform distribution, then the maximum entropy estimate was the most likely empirical distribution among those consistent with the constraints. This principle has been generalized using the Kullback—Leibler separator, I(q,p) between two distributions q and p to the principle of minimum relative entropy [], where this latter principle reduces to the former when p is the uniform distribution. In general, there has been enormous interest in this interplay between statistics and information theory within the communities of statistics [,,], information theory [,,,], and operations research [,,,]." @default.
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- W1597376089 date "1992-01-01" @default.
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- W1597376089 title "Posterior Convergence Under Incomplete Information" @default.
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- W1597376089 doi "https://doi.org/10.1007/978-1-4615-3600-0_16" @default.
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