We consider the problem of asynchronous online testing, aimed at providing control of the false discovery rate (FDR) during a continual stream of data collection and testing, where each test may be a sequential test that can start and stop at arbitrary times. This setting increasingly characterizes real-world applications in science and industry, where teams of researchers across large organizations may conduct tests of hypotheses in a decentralized manner. The overlap in time and space also tends to induce dependencies among test statistics, a challenge for classical methodology, which either assumes (overly optimistically) independence or (overly pessimistically) arbitrary dependence between test statistics. We present a general framework that addresses both of these issues via a unified computational abstraction that we refer to as "conflict sets." We show how this framework yields algorithms with formal FDR guarantees under a more intermediate, local notion of dependence. We illustrate these algorithms in simulation experiments, comparing to existing algorithms for online FDR control.
There is a large and growing literature on false discoveries in multiple testing, aimed at solving a range of problems, often addressing issues of scientific reproducibility in research @cite_8 . Here we focus on work whose methods or objectives have the most overlap with ours. In particular, we focus on literature on online'' methods in multiple testing, and compare and contrast those solutions to the ones we propose. The most salient difference is that we address the general problem of asynchrony; when there is no asynchrony, our approach recovers a slew of existing methods, including work by , , , .
@cite_8
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ABSTRACTMultiple testing problems arising in modern scientific applications can involve simultaneously testing thousands or even millions of hypotheses, with relatively few true signals. In this article, we consider the multiple testing problem where prior information is available (for instance, from an earlier study under different experimental conditions), that can allow us to test the hypotheses as a ranked list to increase the number of discoveries. Given an ordered list of n hypotheses, the aim is to select a data-dependent cutoff k and declare the first k hypotheses to be statistically significant while bounding the false discovery rate (FDR). Generalizing several existing methods, we develop a family of “accumulation tests” to choose a cutoff k that adapts to the amount of signal at the top of the ranked list. We introduce a new method in this family, the HingeExp method, which offers higher power to detect true signals compared to existing techniques. Our theoretical results prove that these metho... In the era of big data, information regarding the same objects can be collected from increasingly more sources. Unfortunately, there usually exist conflicts among the information coming from different sources. To tackle this challenge, truth discovery, i.e., to integrate multi-source noisy information by estimating the reliability of each source, has emerged as a hot topic. In many real world applications, however, the information may come sequentially, and as a consequence, the truth of objects as well as the reliability of sources may be dynamically evolving. Existing truth discovery methods, unfortunately, cannot handle such scenarios. To address this problem, we investigate the temporal relations among both object truths and source reliability, and propose an incremental truth discovery framework that can dynamically update object truths and source weights upon the arrival of new data. Theoretical analysis is provided to show that the proposed method is guaranteed to converge at a fast rate. The experiments on three real world applications and a set of synthetic data demonstrate the advantages of the proposed method over state-of-the-art truth discovery methods. We are concerned with a situation in which we would like to test multiple hypotheses with tests whose p-values cannot be computed explicitly but can be approximated using Monte Carlo simulation. This scenario occurs widely in practice. We are interested in obtaining the same rejections and non-rejections as the ones obtained if the p-values for all hypotheses had been available. The present article introduces a framework for this scenario by providing a generic algorithm for a general multiple testing procedure. We establish conditions that guarantee that the rejections and non-rejections obtained through Monte Carlo simulations are identical to the ones obtained with the p-values. Our framework is applicable to a general class of step-up and step-down procedures, which includes many established multiple testing corrections such as the ones of Bonferroni, Holm, Sidak, Hochberg or Benjamini–Hochberg. Moreover, we show how to use our framework to improve algorithms available in the literature in such a way as to yield theoretical guarantees on their results. These modifications can easily be implemented in practice and lead to a particular way of reporting multiple testing results as three sets together with an error bound on their correctness, demonstrated exemplarily using a real biological dataset. Multiple hypothesis testing is widely used to evaluate scientific studies involving statistical tests. However, for many of these tests, p values are not available and are thus often approximated using Monte Carlo tests such as permutation tests or bootstrap tests. This article presents a simple algorithm based on Thompson Sampling to test multiple hypotheses. It works with arbitrary multiple testing procedures, in particular with step-up and step-down procedures. Its main feature is to sequentially allocate Monte Carlo effort, generating more Monte Carlo samples for tests whose decisions are so far less certain. A simulation study demonstrates that for a low computational effort, the new approach yields a higher power and a higher degree of reproducibility of its results than previously suggested methods.