论文标题
在多个测试和选择性推理中选择和调理
On Selecting and Conditioning in Multiple Testing and Selective Inference
论文作者
论文摘要
我们研究了在选择事件上的选择性推断的一类方法。这样的方法遵循两个阶段的过程。首先，从一些大型假设宇宙中选择了数据驱动的假设（子）集合。随后，推理发生在此数据驱动的集合中，以用于选择的信息为条件。此类方法的示例包括基于基于多面体引理的套索系数的基本数据拆分以及现代数据雕刻方法和选择后推理方法。在本文中，我们将选择，条件和最终错误控制步骤一起作为一种方法，对此类方法采用了整体观点。从这个角度来看，我们证明了直接在整个假设宇宙上定义的多种测试方法至少与基于选择和条件的选择性推理方法一样强大。即使宇宙可能是无限的，并且仅被隐式定义，例如在数据拆分的情况下，该结果也是正确的。我们提供了一个全面的理论框架以及见解，并深入研究了几个案例研究，以说明向非选择性或无条件观点转移的情况，可以产生功率增长。
We investigate a class of methods for selective inference that condition on a selection event. Such methods follow a two-stage process. First, a data-driven (sub)collection of hypotheses is chosen from some large universe of hypotheses. Subsequently, inference takes place within this data-driven collection, conditioned 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 for lasso coefficients based on the polyhedral lemma. In this paper, we adopt a holistic view on such methods, considering the selection, conditioning, and final error control steps together as a single method. From this perspective, we demonstrate that multiple testing methods defined directly on the full universe of hypotheses are always at least as powerful as selective inference methods based on selection and conditioning. This result holds true even when the universe is potentially infinite and only implicitly defined, such as in the case of data splitting. We provide a comprehensive theoretical framework, along with insights, and delve into several case studies to illustrate instances where a shift to a non-selective or unconditional perspective can yield a power gain.
