Bayes factor functions

解释实验和观测研究提供的证据对科学发现过程至关重要。最常用的间接证据衡量标准是P值。不幸的是，P值并不能直接反映新发现的概率，因此经常被误解。贝叶斯因子代表了报告假设检验结果的P值的一种信息性替代方案。它们提供了数据对相互竞争的假设提供的相对支持的直接衡量标准，并能够量化对真零假设的支持。在这个项目中开发的贝叶斯因子函数将从经典测试统计中定义，并将总结支持科学发现的证据。由此得到的贝叶斯因子函数将提供单一实验结果的清晰总结，消除任意的P值阈值，并且是组合来自重复研究的证据的理想选择。它们将提高科学研究的重现性和可复制性。该项目还将为研究生提供研究培训。本项目中开发的贝叶斯因子函数将在几个方面促进贝叶斯测试理论和应用。这些措施包括直接从经典检验统计量(可从标准统计分析中获得)定义贝叶斯因子；将这些检验统计量的分布建模为标准化效应大小(科学和观察性研究中主要感兴趣的数量)的函数；指定科学假设，以便在没有科学/治疗效应的零假设与新的效应或益处之间有明显的区别；以及提供对应于给定效应大小的贝叶斯因子的易于计算的表达式。这些创新将使科学家能够轻松地评估在广泛的科学学科中进行的科学研究产生的统计证据。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.