We investigate a class of methods for selective inference that condition on a selection event. Such methods operate in a two-stage process. First, a (sub)collection of hypotheses is determined in a data-driven way from some large universe of hypotheses. Second, inference is done within the data-driven collection, conditional on the information that was used for the selection. Examples of such methods include basic data splitting, as well as modern data carving methods and post-selection inference methods based on the polyhedral lemma. In this paper, we adopt a holistic view on such methods, viewing the selection, conditioning and final error control steps together as a single method. From this perspective, we show that selective inference methods based on selection and conditioning are always dominated by multiple testing methods defined directly on the full universe of hypotheses. This result even holds when this universe is potentially infinite and only defined implicitly, such as in data splitting. We investigate four case studies of potential power gain from switching to a non-selective and/or an unconditional perspective.

翻译：我们根据选择事件的条件,调查了一组选择性推断方法,这些方法在两阶段过程中运作。首先,从大量假设中以数据驱动的方式,根据数据驱动的方式,从某些大范围的假设中确定假设的(子)集合。第二,在数据驱动的收集中进行推断,以选择时所用的信息为条件。这些方法的例子包括基本数据分离,以及基于多面 Lemma 的现代数据刻录方法和选择后推断方法。在本文中,我们对这种方法采取全面的观点,将选择、调节和最终错误控制步骤作为一个单一的方法一起看待。我们从这个角度表明,基于选择和调节的选择性推断方法总是由直接以整个假设宇宙定义的多重测试方法主导。这一结果甚至在这一宇宙可能具有无限性且仅隐含定义的情况下,例如在数据分离中,仍然有效。我们调查了从转换为非选择性和(或)无条件视角而获得的潜在权力的四项案例研究。