Related papers: Admissible online closed testing must employ e-val…
We propose a method that combines the closed testing framework with the concept of safe anytime-valid inference (SAVI) to compute lower confidence bounds for the true discovery proportion in a multiple testing setting. The proposed…
Can a physicist make only a finite number of errors in the eternal quest to uncover the law of nature? This millennium-old philosophical problem, known as inductive inference, lies at the heart of epistemology. Despite its significance to…
Replicability is central to scientific progress, and the partial conjunction (PC) hypothesis testing framework provides an objective tool to quantify it across disciplines. Existing PC methods assume independent studies. Yet many modern…
This book is written to offer a humble, but unified, treatment of e-values in hypothesis testing. It is organized into three parts: Fundamental Concepts, Core Ideas, and Advanced Topics. The first part includes four chapters that introduce…
Always-valid concentration inequalities are increasingly used as performance measures for online statistical learning, notably in the learning of generative models and supervised learning. Such inequality advances the online learning…
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…
Motivated by recent findings in Li and Zhang (2025), which established an equivalence between certain p-value-based multiple testing procedures and the e-Benjamini-Hochberg procedure (Wang and Ramdas, 2022), we introduce a general framework…
Simultaneous inference allows for the exploration of data while deciding on criteria for proclaiming discoveries. It was recently proved that all admissible post-hoc inference methods for true discoveries must employ closed testing. In this…
We present a unifying approach to multiple testing procedures for sequential (or streaming) data by giving sufficient conditions for a sequential multiple testing procedure to control the familywise error rate (FWER), extending to the…
One of the core applications of machine learning to knowledge discovery consists on building a function (a hypothesis) from a given amount of data (for instance a decision tree or a neural network) such that we can use it afterwards to…
Suppose that at any stage of a statistical experiment a control variable $X$ that affects the distribution of the observed data $Y$ at this stage can be used. The distribution of $Y$ depends on some unknown parameter $\theta$, and we…
Motivation: While the analysis of a single RNA sequencing (RNAseq) dataset has been well described in the literature, modern research workflows often have additional complexity in that related RNAseq experiments are performed sequentially…
E-processes enable hypothesis testing with ongoing data collection while maintaining Type I error control. However, when testing multiple hypotheses simultaneously, current $e$-value based multiple testing methods such as e-BH are not…
A resurgence of interest in multiple hypothesis testing has occurred in the last decade. Motivated by studies in genomics, microarrays, DNA sequencing, drug screening, clinical trials, bioassays, education and psychology, statisticians have…
Hypothesis testing is a key part of empirical science and multiple testing as well as the combination of evidence from several tests are continued areas of research. In this article we consider the problem of combining the results of…
Consider testing multiple hypotheses in the setting where the p-values of all hypotheses are unknown and thus have to be approximated using Monte Carlo simulations. One class of algorithms published in the literature for this scenario…
Biological research often involves testing a growing number of null hypotheses as new data is accumulated over time. We study the problem of online control of the familywise error rate (FWER), that is testing an apriori unbounded sequence…
The e-value is swiftly rising in prominence in many applications of hypothesis testing and multiple testing, yet its relationship to classical testing theory remains elusive. We unify e-values and classical testing into a single 'continuous…
Statistical discoveries are often obtained through multiple hypothesis testing. A variety of procedures exists to evaluate multiple hypotheses, for instance the ones of Benjamini-Hochberg, Bonferroni, Holm or Sidak. We are particularly…
We consider the optimal value of information (VoI) problem, where the goal is to sequentially select a set of tests with a minimal cost, so that one can efficiently make the best decision based on the observed outcomes. Existing algorithms…