arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2406.08892math.STstat.TH
收藏

半 Cauchy 先验下的极小极大性

Minimaxity under the half-Cauchy prior

Yuzo Maruyama, Takeru Matsuda

备注：
The title of this article is quite similar to that of our previous article on arXiv 2308.09339, in which we discussed some variants of the half-Cauchy prior. In this article, we focus on the half-Cauchy prior itself
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

AI总结：

针对二次损失下 p 元正态均值估计问题，本文利用区间算术从理论上证明了半 Cauchy 先验对应的 Bayes 估计量具有极小极大性。

摘要：

本文是 Polson 和 Scott（2012，《Bayesian Analysis》）的后续研究；该文声称半 Cauchy 先验是层次模型中尺度参数的合理默认先验。对于二次损失下 p 元正态均值的估计，他们通过数值实验表明，关于半 Cauchy 先验的 Bayes 估计量似乎具有极小极大性。本文利用区间算术，从理论上确立了相应 Bayes 估计量的极小极大性。

英文摘要：

This is a follow-up paper of Polson and Scott (2012, Bayesian Analysis), which claimed that the half-Cauchy prior is a sensible default prior for a scale parameter in hierarchical models. For estimation of a p-variate normal mean under the quadratic loss, they demonstrated that the Bayes estimator with respect to the half-Cauchy prior seems to be minimax through numerical experiments. In this paper, we theoretically establish the minimaxity of the corresponding Bayes estimator using the interval arithmetric.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑