Bayesian Methodology for Assessing Invariance in Behavioral Data

该项目将侧重于开发贝叶斯因子，这是一种替代传统统计测试的方法。 贝叶斯因子与经典的频率论假设检验方法相比具有天然的优势，因为它们可以评估支持和反对零假设的证据。 然而，贝叶斯分析依赖于研究者提供的一定程度的先验信息。 这种事先的规范可以被看作是调查者在收集数据之前对自然状态的信念的代表，这种主观性程度一直是贝叶斯分析的主要批评。 该项目将开发所谓的“默认”方法，既最大限度地减少对这种主观性的依赖，也提供最佳的统计特性，以测试零假设和反对零假设。 对贝叶斯因子的理论研究将指导缺省先验的选择，物理科学已经通过证明某些关系在所有条件下都成立而取得了进展。 这种关系可以称为不变的。 相反，一些社会科学和行为科学传统上通过证明实验操作产生改变的反应来发现新理论，而不是通过证明反应是不变的。 传统的统计方法已经被开发出来，以证明反应不是不变的刺激，但这些工具是不适合证明不变性。 除了开发传统统计测试的贝叶斯替代方法外，该项目还将开发软件，并通过网络小程序提供，以便研究人员能够方便地使用新的统计工具。 预计这些新的发展将使贝叶斯因子在许多领域中有用和常见，包括流行病学，经济学，心理学，野生动物和生物学。

This project will focus on developing Bayes factors, a methodology that is an alternative to traditional statistical testing. Bayes factors have a natural advantage over classical frequentist hypothesis testing methods in that they can assess the evidence both for and against a null hypothesis. Bayesian analysis, however, relies on a degree of prior information supplied by the investigator. This prior specification can be viewed as representation of the investigator's belief in the state of nature before collecting data, and this degree of subjectivity has been a major criticism of Bayesian analysis. The project will develop so-called "default" methods that both minimize the reliance on this subjectivity and also provide optimal statistical properties in testing both for and against the null hypothesis. The theoretical study of Bayes factors will guide the choice of default prior.The physical sciences have made gains by demonstrating that certain relationships hold across all conditions. These kinds of relationships can be termed invariant. Some social and behavioral sciences, in contrast, traditionally discover new theories by demonstrating that experimental manipulations produce altered responses rather than by proving that the response is unchanged. Conventional statistical methodology has been developed to prove that responses are not invariant to stimuli, but these tools are ill-suited to proving invariance. In addition to the development of a Bayesian alternative to classical statistical testing, the project will develop software and make it available through web applets so that researchers can easily use the new statistical tools. It is anticipated that these new developments will make Bayes factors useful and common in a number of fields, including epidemiology, economics, psychology, wildlife, and biology.