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具有错误覆盖率控制的信息性共形预测集选择AI 解读

Abstract In supervised learning, including regression and classification, conformal methods provide prediction sets for the outcome/label with finite sample coverage for any machine learning predictor. We consider here the case where such prediction sets come after a selection process. The selection process requires that the selected prediction sets be ‘informative’ in a well-defined sense. We consider both the classification and regression settings where the analyst may…

同时方向推断AI 解读

Abstract We consider the problem of inference on the signs of n>1 parameters. We aim to provide 1−α post hoc confidence bounds on the number of positive and negative (or non-positive) parameters, with a simultaneous guarantee, for all subsets of parameters. We suggest to start by using the data to select the direction of the hypothesis test for each parameter; then, adjust the p-values of the one-sided hypotheses for the selection, and use the adjusted p-values for…

多重检验问题的最优与最大最小程序AI 解读

Abstract Multiple testing problems (MTPs) are a staple of modern statistical analysis. The fundamental objective of MTPs is to reject as many false null hypotheses as possible (that is, maximize some notion of power), subject to controlling an overall measure of false discovery, like family-wise error rate (FWER) or false discovery rate (FDR). In this paper we provide generalizations to MTPs of the optimal Neyman-Pearson test for a single hypothesis. We show that for simple…

两组模型中错误发现准则的最优控制AI 解读

Abstract The highly influential two-group model in testing a large number of statistical hypotheses assumes that the test statistics are drawn independently from a mixture of a high probability null distribution and a low probability alternative. Optimal control of the marginal false discovery rate (mFDR), in the sense that it provides maximal power (expected true discoveries) subject to mFDR control, is known to be achieved by thresholding the local false discovery rate…

聚合关联检验后的选择后估计与检验AI 解读

Summary The practice of pooling several individual test statistics to form aggregate tests is common in many statistical applications where individual tests may be underpowered. Although selection by aggregate tests can serve to increase power, the selection process invalidates inference based on the individual test statistics, making it difficult to identify those that drive the signal in follow-up inference. Here, we develop a general approach for valid inference following…

大规模基因组数据中聚合层检验后的选择后推断AI 解读

In many genomic applications, hypotheses tests are performed for powerful identification of signals by aggregating test-statistics across units within naturally defined classes. Following class-level testing, it is naturally of interest to identify the lower level units which contain true signals. Testing the individual units within a class without taking into account the fact that the class was selected using an aggregate-level test-statistic, will produce biased inference.…

评估两项多特征研究中发现的可重复性AI 解读

Replicability analysis aims to identify the overlapping signals across independent studies that examine the same features. For this purpose we develop hypothesis testing procedures that first select the promising features from each of two studies separately. Only those features selected in both studies are then tested. The proposed procedures have theoretical guarantees regarding their control of the familywise error rate or false discovery rate on the replicability claims.…

空间信号的错误发现率控制AI 解读

The problem of multiple testing for the presence of signal in spatial data can involve numerous locations. Traditionally, each location is tested separately for signal presence, but then the findings are reported in terms of clusters of nearby locations. This is an indication that the units of interest for testing are clusters rather than individual locations. The investigator may know a priori these more natural units or an approximation to them. We suggest testing these…