This article focuses on the performance of Bayes estimators, in comparison with the MLE, in multinomial models with a relatively large number of cells. The prior for the Bayes estimator is taken to be the conjugate Dirichlet, i.e., the multivariate Beta, with exchangeable distributions over the coordinates, including the non-informative uniform distribution. The choice of the multinomial is motivated by its many applications in business and industry, but also by its use in providing a simple nonparametric estimator of an unknown distribution. It is striking that the Bayes procedure outperforms the asymptotically efficient MLE over most of the parameter spaces for even moderately large dimensional parameter space and rather large sample sizes.

中文翻译：

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贝叶斯估计量在高维多项式模型中优于 MLE 及其对非参数贝叶斯理论的影响

本文重点介绍贝叶斯估计器与 MLE 相比，在具有相对大量单元格的多项模型中的性能。贝叶斯估计量的先验被认为是共轭狄利克雷，即多元 Beta，在坐标上具有可交换的分布，包括非信息均匀分布。多项式的选择是由于它在商业和工业中的许多应用，而且还因为它用于提供未知分布的简单非参数估计量。令人惊讶的是，即使对于中等大维参数空间和相当大的样本量，贝叶斯过程在大多数参数空间上都优于渐近有效的 MLE。