The flaw of averages: Bayes factors as posterior means of the likelihood ratio.

IF 1.3 4区 医学 Q4 PHARMACOLOGY & PHARMACY Pharmaceutical Statistics Pub Date : 2024-07-01 Epub Date: 2024-01-28 DOI:10.1002/pst.2355
Charles C Liu, Ron Xiaolong Yu, Murray Aitkin
{"title":"The flaw of averages: Bayes factors as posterior means of the likelihood ratio.","authors":"Charles C Liu, Ron Xiaolong Yu, Murray Aitkin","doi":"10.1002/pst.2355","DOIUrl":null,"url":null,"abstract":"<p><p>As an alternative to the Frequentist p-value, the Bayes factor (or ratio of marginal likelihoods) has been regarded as one of the primary tools for Bayesian hypothesis testing. In recent years, several researchers have begun to re-analyze results from prominent medical journals, as well as from trials for FDA-approved drugs, to show that Bayes factors often give divergent conclusions from those of p-values. In this paper, we investigate the claim that Bayes factors are straightforward to interpret as directly quantifying the relative strength of evidence. In particular, we show that for nested hypotheses with consistent priors, the Bayes factor for the null over the alternative hypothesis is the posterior mean of the likelihood ratio. By re-analyzing 39 results previously published in the New England Journal of Medicine, we demonstrate how the posterior distribution of the likelihood ratio can be computed and visualized, providing useful information beyond the posterior mean alone.</p>","PeriodicalId":19934,"journal":{"name":"Pharmaceutical Statistics","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Pharmaceutical Statistics","FirstCategoryId":"3","ListUrlMain":"https://doi.org/10.1002/pst.2355","RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/1/28 0:00:00","PubModel":"Epub","JCR":"Q4","JCRName":"PHARMACOLOGY & PHARMACY","Score":null,"Total":0}
引用次数: 0

Abstract

As an alternative to the Frequentist p-value, the Bayes factor (or ratio of marginal likelihoods) has been regarded as one of the primary tools for Bayesian hypothesis testing. In recent years, several researchers have begun to re-analyze results from prominent medical journals, as well as from trials for FDA-approved drugs, to show that Bayes factors often give divergent conclusions from those of p-values. In this paper, we investigate the claim that Bayes factors are straightforward to interpret as directly quantifying the relative strength of evidence. In particular, we show that for nested hypotheses with consistent priors, the Bayes factor for the null over the alternative hypothesis is the posterior mean of the likelihood ratio. By re-analyzing 39 results previously published in the New England Journal of Medicine, we demonstrate how the posterior distribution of the likelihood ratio can be computed and visualized, providing useful information beyond the posterior mean alone.

查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
平均值的缺陷:贝叶斯因子作为似然比的后验手段。
贝叶斯因子(或边际似然比)作为频数法 p 值的替代方法,一直被视为贝叶斯假设检验的主要工具之一。近年来,一些研究人员开始重新分析著名医学期刊以及美国食品与药物管理局批准药物试验的结果,结果表明贝叶斯因子得出的结论往往与 p 值不同。在本文中,我们研究了贝叶斯系数可直接量化证据相对强度的说法。特别是,我们证明,对于具有一致先验的嵌套假设,零假设相对于备择假设的贝叶斯因子是似然比的后验平均值。通过重新分析之前发表在《新英格兰医学杂志》上的 39 项结果,我们展示了如何计算似然比的后验分布并将其可视化,从而提供了超越后验平均值的有用信息。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
Pharmaceutical Statistics
Pharmaceutical Statistics 医学-统计学与概率论
CiteScore
2.70
自引率
6.70%
发文量
90
审稿时长
6-12 weeks
期刊介绍: Pharmaceutical Statistics is an industry-led initiative, tackling real problems in statistical applications. The Journal publishes papers that share experiences in the practical application of statistics within the pharmaceutical industry. It covers all aspects of pharmaceutical statistical applications from discovery, through pre-clinical development, clinical development, post-marketing surveillance, consumer health, production, epidemiology, and health economics. The Journal is both international and multidisciplinary. It includes high quality practical papers, case studies and review papers.
期刊最新文献
Optimizing Sample Size Determinations for Phase 3 Clinical Trials in Type 2 Diabetes. Prediction Intervals for Overdispersed Poisson Data and Their Application in Medical and Pre-Clinical Quality Control. Treatment Effect Measures Under Nonproportional Hazards. Bayesian Response Adaptive Randomization for Randomized Clinical Trials With Continuous Outcomes: The Role of Covariate Adjustment. PKBOIN-12: A Bayesian Optimal Interval Phase I/II Design Incorporating Pharmacokinetics Outcomes to Find the Optimal Biological Dose.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1