On the uniform consistency of Bayes estimates for multinomial probabilities
On the uniform consistency of Bayes estimates for multinomial probabilities
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关于多项概率贝叶斯估计的一致一致性
DOI：
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发表时间：
1990
期刊：
影响因子：
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通讯作者：
D. Freedman
中科院分区：
文献类型：
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作者：
P. Diaconis;D. Freedman
一个k边骰子掷n次，以估计概率θ 1，...，各侧着陆的θ k。θ的最大似然估计是经验比例p=（p 1，.，p k）。考虑一个贝叶斯集，它在参数空间的所有合理子集上放置一致正的先验质量。它们的后验分布将均匀地集中在p附近。这些界限适用于所有样本序列：没有异常的空集
A k-sided die is thrown n times, to estimate the probabilities θ 1 , ..., θ k of landing on the various sides. The MLE of θ is the vector of empirical proportions p=(p 1 , ..., 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