Related papers: Control of Directional Errors in Fixed Sequence Mu…
Motivated by the practice of exploratory research, we formulate an approach to multiple testing that reverses the conventional roles of the user and the multiple testing procedure. Traditionally, the user chooses the error criterion, and…
There has been a misconception that only one type of error rate control is necessary in clinical trials, leading to debates over whether to prioritize Familywise Error Rate (FWER) or False Discovery Rate (FDR). This misconception has led to…
The sequential multiple testing problem is considered under two generalized error metrics. Under the first one, the probability of at least $k$ mistakes, of any kind, is controlled. Under the second, the probabilities of at least $k_1$…
The partial conjunction null hypothesis is tested in order to discover a signal that is present in multiple studies. The standard approach of carrying out a multiple test procedure on the partial conjunction (PC) $p$-values can be extremely…
Diagnostic accuracy studies assess sensitivity and specificity of a new index test in relation to an established comparator or the reference standard. The development and selection of the index test is usually assumed to be conducted prior…
We consider the problem of identifying whether findings replicate from one study of high dimension to another, when the primary study guides the selection of hypotheses to be examined in the follow-up study as well as when there is no…
A new online multiple testing procedure is described in the context of anomaly detection, which controls the False Discovery Rate (FDR). An accurate anomaly detector must control the false positive rate at a prescribed level while keeping…
Closed testing procedures are classically used for familywise error rate (FWER) control, but they can also be used to obtain simultaneous confidence bounds for the false discovery proportion (FDP) in all subsets of the hypotheses. In this…
In this paper we propose a computationally efficient multiple hypothesis testing procedure for persistent homology. The computational efficiency of our procedure is based on the observation that one can empirically simulate a null…
Multiple hypotheses testing is a core problem in statistical inference and arises in almost every scientific field. Given a sequence of null hypotheses $\mathcal{H}(n) = (H_1,..., H_n)$, Benjamini and Hochberg…
Most scientific disciplines use significance testing to draw conclusions about experimental or observational data. This classical approach provides a theoretical guarantee for controlling the number of false positives across a set of…
The double hypothesis test (DHT) is a test that allows controlling Type I (producer) and Type II (consumer) errors. It is possible to say whether the batch has a defect rate, p, between 1.5 and 2%, or between 2 and 5%, or between 5 and 10%,…
The traditional approaches to false discovery rate (FDR) control in multiple hypothesis testing are usually based on the null distribution of a test statistic. However, all types of null distributions, including the theoretical,…
We introduce a multiple testing procedure (TreeBH) which addresses the challenge of controlling error rates at multiple levels of resolution. Conceptually, we frame this problem as the selection of hypotheses which are organized…
Familywise error rate (FWER) has been a cornerstone in simultaneous inference for decades, and the classical Bonferroni method has been one of the most prominent frequentist approaches for controlling FWER. The present article studies the…
In multiple testing several criteria to control for type I errors exist. The false discovery rate, which evaluates the expected proportion of false discoveries among the rejected null hypotheses, has become the standard approach in this…
The introduction of the false discovery rate (FDR) by Benjamini and Hochberg has spurred a great interest in developing methodologies to control the FDR in various settings. The majority of existing approaches, however, address the FDR…
The problem of multiple hypothesis testing with observation control is considered in both fixed sample size and sequential settings. In the fixed sample size setting, for binary hypothesis testing, the optimal exponent for the maximal error…
In many scenarios such as genome-wide association studies where dependences between variables commonly exist, it is often of interest to infer the interaction effects in the model. However, testing pairwise interactions among millions of…
In the context of multiple hypotheses testing, the proportion $\pi_0$ of true null hypotheses in the pool of hypotheses to test often plays a crucial role, although it is generally unknown a priori. A testing procedure using an implicit or…