Selective inference is the problem of giving valid answers to statistical questions chosen in a data-driven manner. A standard solution to selective inference is simultaneous inference, which delivers valid answers to the set of all questions that could possibly have been asked. However, simultaneous inference can be unnecessarily conservative if this set includes many questions that were unlikely to be asked in the first place. We introduce a less conservative solution to selective inference that we call locally simultaneous inference, which only answers those questions that could plausibly have been asked in light of the observed data, all the while preserving rigorous type I error guarantees. For example, if the objective is to construct a confidence interval for the "winning" treatment effect in a clinical trial with multiple treatments, and it is obvious in hindsight that only one treatment had a chance to win, then our approach will return an interval that is nearly the same as the uncorrected, standard interval. Compared to conditional selective inference, which demands stronger, conditional guarantees, locally simultaneous inference is more easily applicable in nonparametric settings and is more numerically stable.
翻译:选择性推论是对以数据驱动方式选择的统计问题给出有效答案的问题。 选择性推论的标准解决办法是同时推论,它对可能问出的所有问题组提供有效答案。 但是,如果这组问题组包括最初不可能问到的许多问题,同时推论可能是不必要保守的。 我们采用较保守的解决方法来解决我们称为本地同时推论的选择性推论,这种推论只回答那些根据观察到的数据可以合理提出的问题,所有问题都保留严格的I型错误保证。例如,如果目标是在临床试验中为多重治疗的“结对”治疗效果建立一个信任间隔,而且事后看来只有一种治疗有机会获胜,那么我们的方法就会返回一个几乎与未纠正的标准间隔相同的间隔。比较于有条件的选择性推论,要求更强、有条件的保证,当地同时推论在非对称环境中更容易适用,并且更具有数字稳定性。