Bayesian inference and testing any hypothesis you can specify

Hypothesis testing is a special form of model selection. Once a pair of competing models is fully defined, their definition immediately leads to a measure of how strongly each model supports the data. The ratio of their support is often called the likelihood ratio or the Bayes factor. Critical in the model selection endeavor is the specification of the models. In the case of hypothesis testing, it is of the greatest importance that we specify exactly what is meant by a "null" hypothesis as well as the alternative to which it is contrasted, and that these are suitable instantiations of theoretical positions. Here, we provide an overview of different instantiations of null and alternative hypotheses that can be useful in practice, while the underlying method of likelihood comparison is universal and identical in all cases. An associated app can be found via https://osf.io/mvp53/.

假设检验是模型选择的一种特殊形式。一旦一对竞争性模型被完全定义，它们的定义随即导出对每份数据支持强度的度量。它们支持之比常被称作似然比或贝叶斯因子。在模型选择的过程中，明确模型的规格至关重要。在假设检验的情况下，精确界定“零假设”及其与之相对的备择假设尤为关键，并确保这些假设是对理论立场的适宜体现。在此，我们概述了不同实例化的零假设和备择假设，这些在实践中有助于理解，而基于似然比较的底层方法在所有情况下都是通用的且一致的。相关应用程序可通过https://osf.io/mvp53/获取。