Related papers: Error-rate and decision-theoretic methods of multi…
The mitigation of false positives is an important issue when conducting multiple hypothesis testing. The most popular paradigm for false positives mitigation in high-dimensional applications is via the control of the false discovery rate…
A previously proved theorem gives sufficient conditions for an estimator of the false discovery rate (FDR) to conservatively converge to the FDR with probability 1 as the number of hypothesis tests increases, even for small sample sizes. It…
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.…
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 present paper establishes new multiple procedures for simultaneous testing of a large number of hypotheses under dependence. Special attention is devoted to experiments with rare false hypotheses. This sparsity assumption is typically…
In this article, we propose a new method for the fundamental task of testing for dependence between two groups of variables. The response densities under the null hypothesis of independence and the alternative hypothesis of dependence are…
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.…
A popular approach to significance testing proposes to decide whether the given hypothesized statistical model is likely to be true (or false). Statistical decision theory provides a basis for this approach by requiring every significance…
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…
Statistical dependence between hypotheses poses a significant challenge to the stability of large scale multiple hypotheses testing. Ignoring it often results in an unacceptably large spread in the false positive proportion even though the…
Modern scientific technology has provided a new class of large-scale simultaneous inference problems, with thousands of hypothesis tests to consider at the same time. Microarrays epitomize this type of technology, but similar situations…
We consider statistical hypothesis testing simultaneously over a fairly general, possibly uncountably infinite, set of null hypotheses, under the assumption that a suitable single test (and corresponding $p$-value) is known for each…
The analysis of large-scale datasets, especially in biomedical contexts, frequently involves a principled screening of multiple hypotheses. The celebrated two-group model jointly models the distribution of the test statistics with mixtures…
A/B testing is ubiquitous within the machine learning and data science operations of internet companies. Generically, the idea is to perform a statistical test of the hypothesis that a new feature is better than the existing platform---for…
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…
Genetic investigations often involve the testing of vast numbers of related hypotheses simultaneously. To control the overall error rate, a substantial penalty is required, making it difficult to detect signals of moderate strength. To…
Current statistical inference problems in areas like astronomy, genomics, and marketing routinely involve the simultaneous testing of thousands -- even millions -- of null hypotheses. For high-dimensional multivariate distributions, these…
The positive false discovery rate (pFDR) is a useful overall measure of errors for multiple hypothesis testing, especially when the underlying goal is to attain one or more discoveries. Control of pFDR critically depends on how much…
Multiple testing problems are a staple of modern statistical analysis. The fundamental objective of multiple testing procedures is to reject as many false null hypotheses as possible (that is, maximize some notion of power), subject to…
Refining one's hypotheses in the light of data is a common scientific practice; however, the dependency on the data introduces selection bias and can lead to specious statistical analysis. An approach for addressing this is via conditioning…