标题： 关于事后假设检验中的可接受性 显示英文标题

标题： On admissibility in post-hoc hypothesis testing

摘要： 经典假设检验的有效性要求显著性水平$\alpha$在任何统计分析之前固定。这是一个严格的要求。例如，它禁止在实验过程中（或之后）由于对假阳性成本的关注发生变化而更新$\alpha$，或者为了反映意外的强烈证据反对原假设。也许最令人不安的是，观察到一个 p 值$p\ll\alpha$与$p\leq \alpha$相比对于任何后续决策都没有（统计）相关性。根据 Grünwald (2024) 的最新工作，我们发展了一种事后假设检验理论，使得$\alpha$可以在查看和分析数据之后选择。为了研究“良好”的事后检验，我们引入了$\Gamma$-可接受性，其中$\Gamma$是一个将数据映射到显著性水平的对手集合。 一个测试是$\Gamma$可接受的，大致来说，如果在$\Gamma$中不存在其他测试在所有对手上表现至少一样好甚至有时更好。 对于点零假设和备择假设，我们证明了任何$\Gamma$可接受测试的一般性质，对于任何$\Gamma$，它们必须基于 e 值。 我们还对各种特定的$\Gamma$分类了可接受测试的集合。 显示英文摘要

摘要： The validity of classical hypothesis testing requires the significance level $\alpha$ be fixed before any statistical analysis takes place. This is a stringent requirement. For instance, it prohibits updating $\alpha$ during (or after) an experiment due to changing concern about the cost of false positives, or to reflect unexpectedly strong evidence against the null. Perhaps most disturbingly, witnessing a p-value $p\ll\alpha$ vs $p\leq \alpha$ has no (statistical) relevance for any downstream decision-making. Following recent work of Gr\"unwald (2024), we develop a theory of post-hoc hypothesis testing, enabling $\alpha$ to be chosen after seeing and analyzing the data. To study "good" post-hoc tests we introduce $\Gamma$-admissibility, where $\Gamma$ is a set of adversaries which map the data to a significance level. A test is $\Gamma$-admissible if, roughly speaking, there is no other test which performs at least as well and sometimes better across all adversaries in $\Gamma$. For point nulls and alternatives, we prove general properties of any $\Gamma$-admissible test for any $\Gamma$ and show that they must be based on e-values. We also classify the set of admissible tests for various specific $\Gamma$.