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The Polya Urn: Limit Theorems, Polya Divergence, Maximum Entropy and Maximum Probability

Marian Grendar·Robert K. Niven
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Abstract

Sanov's Theorem and the Conditional Limit Theorem (CoLT) are established for a multicolor Polya Eggenberger urn sampling scheme, giving the Polya divergence and the Polya extension to the Maximum Relative Entropy (MaxEnt) method. Polya MaxEnt includes the standard MaxEnt as a special case. The universality of standard MaxEnt - advocated by an axiomatic approach to inference for inverse problems - is challenged, in favor of a probabilistic approach based on CoLT and the Maximum Probability principle.

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Marian Grendar, Robert K. Niven. 2006-12-29. The Polya Urn: Limit Theorems, Polya Divergence, Maximum Entropy and Maximum Probability. https://arxiv.org/abs/cond-mat/0612697

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