标题： beyond 尼曼-皮尔逊：e 值启用带有数据驱动 α 的假设检验 显示英文标题

标题： Beyond Neyman-Pearson: e-values enable hypothesis testing with a data-driven alpha

摘要： 统计假设检验中的一个标准做法是在接受/拒绝决策的同时提到 p 值。我们展示了提及 e 值的优点。使用 p 值时，不清楚如何利用极端观测值（例如，p $\ll \alpha$）来获得更好的频率决策。而使用 e 值则很简单，因为在广义的 Neyman-Pearson 设置中，它们提供了 Type-I 风险控制，并且决策任务（一般损失函数）是在观察数据后事后确定的——从而为“游走的 $\alpha$”提供了一个切入点。当考虑 Type-II 风险时，事后设置中唯一可接受的决策规则最终是基于 e 值的。同样地，如果指定有缺陷的置信区间所导致的损失事先未固定，标准的置信区间和分布可能会失效，而 e-置信集和 e-后验仍然能提供有效的风险保证。现在，针对一系列经典的检验问题，已经开发出了足够强大的 e 值。我们讨论了更广泛应用和部署的主要挑战。 显示英文摘要

摘要： A standard practice in statistical hypothesis testing is to mention the p-value alongside the accept/reject decision. We show the advantages of mentioning an e-value instead. With p-values, it is not clear how to use an extreme observation (e.g. p $\ll \alpha$) for getting better frequentist decisions. With e-values it is straightforward, since they provide Type-I risk control in a generalized Neyman-Pearson setting with the decision task (a general loss function) determined post-hoc, after observation of the data -- thereby providing a handle on `roving $\alpha$'s'. When Type-II risks are taken into consideration, the only admissible decision rules in the post-hoc setting turn out to be e-value-based. Similarly, if the loss incurred when specifying a faulty confidence interval is not fixed in advance, standard confidence intervals and distributions may fail whereas e-confidence sets and e-posteriors still provide valid risk guarantees. Sufficiently powerful e-values have by now been developed for a range of classical testing problems. We discuss the main challenges for wider development and deployment.