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September, 1990 On the Uniform Consistency of Bayes Estimates for Multinomial Probabilities
P. Diaconis, D. Freedman
Ann. Statist. 18(3): 1317-1327 (September, 1990). DOI: 10.1214/aos/1176347751

Abstract

A $k$-sided die is thrown $n$ times, to estimate the probabilities $\theta_1, \ldots, \theta_k$ of landing on the various sides. The MLE of $\theta$ is the vector of empirical proportions $p = (p_1, \ldots, p_k)$. Consider a set of Bayesians that put uniformly positive prior mass on all reasonable subsets of the parameter space. Their posterior distributions will be uniformly concentrated near $p$. Sharp bounds are given, using entropy. These bounds apply to all sample sequences: There are no exceptional null sets.

Citation

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P. Diaconis. D. Freedman. "On the Uniform Consistency of Bayes Estimates for Multinomial Probabilities." Ann. Statist. 18 (3) 1317 - 1327, September, 1990. https://doi.org/10.1214/aos/1176347751

Information

Published: September, 1990
First available in Project Euclid: 12 April 2007

zbMATH: 0788.62005
MathSciNet: MR1062710
Digital Object Identifier: 10.1214/aos/1176347751

Subjects:
Primary: 62A15
Secondary: 62E20

Rights: Copyright © 1990 Institute of Mathematical Statistics

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Vol.18 • No. 3 • September, 1990
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