Bayes factor functions

贝叶斯因子函数

• 批准号: 2311005
• 负责人: Valen Johnson
• 金额: $ 35万
• 依托单位: Texas A&M University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-09-01 至 2026-08-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2311005&HistoricalAwards=false
• 关键词: Bayes; factor; functions

Interpreting the evidence provided by experimental and observational studies is essential to the process of scientific discovery. The most commonly used indirect measures of evidence are P-values. Unfortunately, P-values do not directly reflect the probability that a new discovery has been made and are often mis-interpreted. Bayes factors represent an informative alternative to P-values for reporting outcomes of hypothesis tests. They provide direct measures of the relative support that data provide to competing hypotheses and are able to quantify support for true null hypotheses. The Bayes factor functions developed in this project will be defined from classical test statistics and will summarize evidence in support of scientific discoveries. The resulting Bayes factor functions will provide clear summaries of the outcome from a single experiment, eliminate arbitrary P-value thresholds, and are ideal for combining evidence from replicated studies. They will enhance both the reproducibility and replicability of scientific studies. The project will also provide research training for graduate students. The Bayes factor functions developed in this project will advance Bayesian testing theory and application in several ways. These include defining Bayes factors directly from classical test statistics (which are readily available from standard statistical analyses); modeling the distributions of these test statistics as functions of standardized effect sizes (the quantities of primary interest in scientific and observational studies); specifying scientific hypotheses so that there is a clear distinction between the null hypothesis of no scientific/treatment effect versus a new effect or benefit; and providing easily calculable expressions for the Bayes factors corresponding to given effect sizes. These innovations will allow scientists to easily assess statistical evidence arising from scientific studies conducted across a wide range of scientific disciplines.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

解释实验和观察研究提供的证据对科学发现的过程至关重要。 最常用的间接证据测量是P值。 不幸的是，P值并不能直接反映新发现的概率，而且经常被误解。 贝叶斯因子代表用于报告假设检验结果的P值的信息替代。它们提供了数据对竞争假设的相对支持的直接测量，并且能够量化对真实零假设的支持。 在这个项目中开发的贝叶斯因子函数将从经典的测试统计中定义，并将总结支持科学发现的证据。 由此产生的贝叶斯因子函数将提供单个实验结果的清晰摘要，消除任意的P值阈值，并且非常适合结合来自重复研究的证据。 它们将提高科学研究的再现性和可复制性。该项目还将为研究生提供研究培训。本计画所发展之贝氏因子函数，将在多方面促进贝氏测验理论与应用。 这些包括直接从经典的测试统计定义贝叶斯因子（可从标准统计分析中轻松获得）;将这些检验统计量的分布建模为标准化效应量的函数（科学和观察研究中主要关注的数量）;具体说明科学假设，以便明确区分无科学假设的零假设和无科学假设的零假设。治疗效果与新的效果或益处;以及提供与给定效果大小对应的贝叶斯因子的容易计算的表达式。这些创新将使科学家能够轻松地评估从广泛的科学学科进行的科学研究中产生的统计证据。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。