Related papers: Controlling the number of significant effects in m…
Multiple hypothesis testing, a situation when we wish to consider many hypotheses, is a core problem in statistical inference that arises in almost every scientific field. In this setting, controlling the false discovery rate (FDR), which…
In hypothesis testing, a false discovery occurs when a hypothesis is incorrectly rejected due to noise in the sample. When adaptively testing multiple hypotheses, the probability of a false discovery increases as more tests are performed.…
Consider the multiple testing problem of testing null hypotheses $H_1,...,H_s$. A classical approach to dealing with the multiplicity problem is to restrict attention to procedures that control the familywise error rate ($\mathit{FWER}$),…
Despite the popularity of the false discovery rate (FDR) as an error control metric for large-scale multiple testing, its close Bayesian counterpart the local false discovery rate (lfdr), defined as the posterior probability that a…
Negative control is a common technique in scientific investigations and broadly refers to the situation where a null effect (''negative result'') is expected. Motivated by a real proteomic dataset, we will present three promising and…
This paper presents a survey on some recent advances for the type I error rate control in multiple testing methodology. We consider the problem of controlling the $k$-family-wise error rate (kFWER, probability to make $k$ false discoveries…
When testing many hypotheses, often we do not have strong expectations about the directions of the effects. In some situations however, the alternative hypotheses are that the parameters lie in a certain direction or interval, and it is in…
The influential claim that most published results are false raised concerns about the trustworthiness and integrity of science. Since then, there have been numerous attempts to examine the rate of false-positive results that have failed to…
We consider the problem of estimating the number of false null hypotheses among a very large number of independently tested hypotheses, focusing on the situation in which the proportion of false null hypotheses is very small. We propose a…
The high fraction of published results that turn out to be incorrect is a major concern of today's science. This paper contributes to the understanding of this problem in two independent directions. First, Johnson's recent claim that…
Recent tools for interactive data exploration significantly increase the chance that users make false discoveries. The crux is that these tools implicitly allow the user to test a large body of different hypotheses with just a few clicks…
Multiple tests are designed to test a whole collection of null hypotheses simultaneously. Their quality is often judged by the false discovery rate (FDR), i.e. the expectation of the quotient of the number of false rejections divided by the…
In a recent simulation study, Goodman et al. (2019) compare several methods with regard to their type I and type II error rates in case of a thick null hypothesis that includes all values that are practically equivalent to the point null…
In large scale multiple testing problems, a two-class empirical Bayes approach can be used to control the false discovery rate (Fdr) for the entire array of hypotheses under study. A sample splitting step is incorporated to modify that…
Multivariate statistics are often available as well as necessary in hypothesis tests. We study how to use such statistics to control not only false discovery rate (FDR) but also positive FDR (pFDR) with good power. We show that FDR can be…
When dealing with the problem of simultaneously testing a large number of null hypotheses, a natural testing strategy is to first reduce the number of tested hypotheses by some selection (screening or filtering) process, and then to…
We present a procedure for controlling FWER when sequentially considering successive subfamilies of null hypotheses and rejecting at most one from each subfamily. Our procedure differs from previous procedures for controlling FWER by…
Multiple hypothesis testing is a core problem in statistical inference and arises in almost every scientific field. Given a set of null hypotheses $\mathcal{H}(n) = (H_1,\dotsc, H_n)$, Benjamini and Hochberg introduced the false discovery…
Controlling the false discovery rate (FDR) is a powerful approach to multiple testing. In many applications, the tested hypotheses have an inherent hierarchical structure. In this paper, we focus on the fixed sequence structure where the…
The use of weights provides an effective strategy to incorporate prior domain knowledge in large-scale inference. This paper studies weighted multiple testing in a decision-theoretic framework. We develop oracle and data-driven procedures…