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Chakrabarti, C. G.; Das, N. C.; De, Kajal

doi:10.1023/a:1019809420269

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“…A particular proposal for least-informative priors are the so-called "entropic priors" [8] [9] [10] [11] [12] [13],that have first been derived by Skilling [8]from the axioms of Maximum Entropy and an additional "quantification" argument. Entropic priors Pa{9) = P{9) owe their name to the shape of their density…”

Section: From Bayes To Entropic Priorsmentioning

confidence: 99%

Bayesian Inference Featuring Entropic Priors

Neumann¹

2007

AIP Conference Proceedings

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The subject of this work is the parametric inference problem, i.e. how to infer from data on the parameters of the data hkelihood of a random process whose parametric form is known a priori. The assumption that Bayes' theorem has to be used to add new data samples reduces the problem to the question of how to specify a prior before having seen any data. For this subproblem three theorems are stated. The first one is that Jaynes' Maximum Entropy Principle requires at least a constraint on the expected data likelihood entropy, which gives entropic priors without the need of further axioms. Second I show that maximizing Shannon entropy under an expected data likelihood entropy constraint is equivalent to maximizing relative entropy and therefore reparametrization invariant for continuous-valued data likelihoods. Third, I propose that in the state of absolute ignorance of the data likelihood entropy, one should choose the hyperparameter a of an entropic prior such that the change of expected data likelihood entropy is maximized. Among other beautiful properties, this principle is equivalent to the maximization of the mean-squared entropy error and invariant against any reparametrizations of the data likelihood. Altogether we get a Bayesian inference procedure that incorporates special prior knowledge if available but has also a sound solution if not, and leaves no hyperparameters unspecified.

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Section: From Bayes To Entropic Priorsmentioning

confidence: 99%

Bayesian Inference Featuring Entropic Priors

Neumann¹

2007

AIP Conference Proceedings

View full text Add to dashboard Cite

show abstract

Untitled

Cited by 1 publication

References 10 publications

Bayesian Inference Featuring Entropic Priors

Bayesian Inference Featuring Entropic Priors

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