You are not currently logged in.
Access JSTOR through your library or other institution:
If You Use a Screen ReaderThis content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
On the Uniform Consistency of Bayes Estimates for Multinomial Probabilities
P. Diaconis and D. Freedman
The Annals of Statistics
Vol. 18, No. 3 (Sep., 1990), pp. 1317-1327
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2242054
Page Count: 11
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Preview not available
A k-sided die is thrown n times, to estimate the probabilities θ1, ..., θk of landing on the various sides. The MLE of θ is the vector of empirical proportions p = (p1, ..., pk). 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.
The Annals of Statistics © 1990 Institute of Mathematical Statistics