Response to the comment Confidence in confidence distributions!
Response to the comment Confidence in confidence distributions!
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回复评论置信度分布的置信度！
DOI：
10.1098/rspa.2020.0579
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Ferson, Scott
中科院分区：
文献类型：
--
作者：
Martin, Ryan;Balch, Michael S.;Ferson, Scott
感谢Céline Cunen博士、Nils Lid Hjort博士和Tore Schweder博士对我们最近关于卫星会合分析中概率稀释现象的贡献[1]以及更一般地说，与使用普通或精确概率表示统计推断相关的困难的兴趣。我们的分析主要集中在贝叶斯不确定性量化上，但当然，这不是唯一可用的概率方法，所以我们欢迎那些写了关于置信分布的书的人提出基于置信分布的解决方案[2]。他们的插图再现了缺乏适当的校准或虚假的信心，可以出现边缘化贝叶斯后验分布时，并强调贝叶斯后验和置信分布（CD）之间的差异，在我们的论文中主张的有效性属性。然而，Cunen et al. [3]-用CD取代贝叶斯后验分布是克服虚假信心所需的一切-可能具有误导性。我们的错误置信度定理适用于所有的认知概率分布，包括CD;因此，与作者的主张相反，他们提出的CD也有错误置信度的风险。特别是，众所周知，CD只支持对形式为（−∞，a]或[a，+∞）的单侧命题的可靠推论。其他集合，包括双侧区间及其补集，仍然受到Balch等人发现的假置信现象的影响。[1]的文件。
Thanks to Drs Céline Cunen, Nils Lid Hjort and Tore Schweder for their interest in our recent contribution [1] concerning the probability dilution phenomenon in satellite conjunction analysis and, more generally, the difficulties associated with representing statistical inference using ordinary or precise probabilities. Our analysis focused primarily on Bayesian uncertainty quantification but, of course, this is not the only probabilistic approach available, so we welcome a confidence distribution-based solution from those who literally wrote the book on confidence distributions [2]. Their illustration reproduces the lack of proper calibration—or false confidence—that can emerge when marginalizing a Bayesian posterior distribution and highlights the difference between Bayesian posteriors and confidence distributions (CDs) with respect to the validity property advocated in our paper. However, the message presented by Cunen et al.[3]—that replacing a Bayesian posterior distribution with a CD is all it takes to overcome false confidence—is potentially misleading. Our false confidence theorem applies to all epistemic probability distributions, including CDs; so, contrary to the authors’ claim, their proposed CD is at risk of false confidence too. In particular, as is well known, CDs only support reliable inferences on one-sided propositions of the form (−∞, a] or [a,+∞). Other sets, including two-sided intervals and their complements, are still subject to the false confidence phenomenon uncovered in Balch et al.[1].
对置信分布的置信度！
DOI：
10.1098/rspa.2019.0781
发表时间：
2020
期刊：
Proceedings of the Royal Society A
影响因子：
--
作者：
Céline Cunen;N. Hjort;T. Schweder
通讯作者：
T. Schweder
频率校准信念函数：回顾和新见解
影响因子：
3.9
作者：
T. Denoeux;Shoumei Li
通讯作者：
Shoumei Li
影响因子：
5.7
作者：
Fraser, D. A. S.
通讯作者：
Fraser, D. A. S.