Defining a Credible Interval Is Not Always Possible with “Point-Null” Priors: A Lesser-Known Correlate of the Jeffreys-Lindley Paradox

IF 4.9 2区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Bayesian Analysis Pub Date : 2022-09-30 DOI:10.1214/23-ba1397

Harlan Campbell, P. Gustafson

引用次数: 2

Abstract

In many common situations, a Bayesian credible interval will be, given the same data, very similar to a frequentist confidence interval, and researchers will interpret these intervals in a similar fashion. However, no predictable similarity exists when credible intervals are based on model-averaged posteriors whenever one of the two nested models under consideration is a so called ''point-null''. Not only can this model-averaged credible interval be quite different than the frequentist confidence interval, in some cases it may be undefined. This is a lesser-known correlate of the Jeffreys-Lindley paradox and is of particular interest given the popularity of the Bayes factor for testing point-null hypotheses.

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用“零点”先验定义可信区间并不总是可能的：Jeffrey-Lindley悖论的一个鲜为人知的相关性

在许多常见情况下，给定相同的数据，贝叶斯可信区间将与频率置信区间非常相似，研究人员将以类似的方式解释这些区间。然而，当考虑的两个嵌套模型中的一个是所谓的“点零”时，基于模型平均后验的可信区间不存在可预测的相似性。这种模型平均可信区间不仅可能与频率置信区间有很大不同，在某些情况下，它可能是未定义的。这是Jeffreys-Lindley悖论的一个鲜为人知的关联，考虑到用于检验点零假设的贝叶斯因子的流行，这是特别有趣的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Bayesian Analysis 数学-数学跨学科应用

CiteScore

6.50

自引率

13.60%

发文量

审稿时长

>12 weeks

期刊介绍： Bayesian Analysis is an electronic journal of the International Society for Bayesian Analysis. It seeks to publish a wide range of articles that demonstrate or discuss Bayesian methods in some theoretical or applied context. The journal welcomes submissions involving presentation of new computational and statistical methods; critical reviews and discussions of existing approaches; historical perspectives; description of important scientific or policy application areas; case studies; and methods for experimental design, data collection, data sharing, or data mining. Evaluation of submissions is based on importance of content and effectiveness of communication. Discussion papers are typically chosen by the Editor in Chief, or suggested by an Editor, among the regular submissions. In addition, the Journal encourages individual authors to submit manuscripts for consideration as discussion papers.