Selective Inference on Multiple Families of Hypotheses

Benjamini, Yoav; Bogomolov, Marina

doi:10.1111/rssb.12028

Cited by 108 publications

(202 citation statements)

References 26 publications

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“…), we have implemented in TreeQTL a multi-resolution approach based on results in Benjamini and Bogomolov (2014) whose practical effectiveness in GWAS has been described in Peterson et al (2016). Furthermore, TreeQTL has the potential to increase power: by focusing on the promising SNPs with possibly higher proportions of true eAssociations, one capitalizes on the adaptivity of FDR.…”

Section: Approachmentioning

confidence: 99%

TreeQTL: hierarchical error control for eQTL findings

et al. 2016

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Summary: Commonly used multiplicity adjustments fail to control the error rate for reported findings in many expression quantitative trait loci (eQTL) studies. TreeQTL implements a hierarchical multiple testing procedure which allows control of appropriate error rates defined relative to a grouping of the eQTL hypotheses. Availability and Implementation: The R package TreeQTL is available for download at

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Section: Approachmentioning

confidence: 99%

TreeQTL: hierarchical error control for eQTL findings

et al. 2016

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“…For m hypothesis (i.e. number of tests performed), the Bonferroni (equation 3), Benjamini-Hochberg (Equation 4) and Benjamini-Yekutieli (Equation 5) procedures [16][17][18] are defined as follows: …”

Section: Equationmentioning

confidence: 99%

“…14,15 Since in these studies thousands of variables can be surveyed at once, multiple hypotheses testing corrections must be performed, for example by controlling the family wise error rate (FWER) or false discovery rate (FDR). [16][17][18] These issues complicate the task of designing an experiment with the adequate sample size to precisely detect and estimate the magnitude of a metabolic effect.…”

Section: Introductionmentioning

confidence: 99%

Power Analysis and Sample Size Determination in Metabolic Phenotyping

et al. 2016

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Estimation of statistical power and sample size is a key aspect of experimental design.However, in metabolic phenotyping, there is currently no accepted approach for these tasks, in large part due to the unknown nature of the expected effect. In such hypothesis free science, neither the number or class of important analytes, nor the effect size are known a priori. We introduce a new approach, based on multivariate simulation, which deals effectively with the highly correlated structure and high-dimensionality of metabolic phenotyping data. First, a large data set is simulated based on the characteristics of a pilot study investigating a given biomedical issue. An effect of a given size, corresponding either to a discrete (classification) or continuous (regression) outcome is then added. Different sample sizes are modeled by randomly selecting data sets of various sizes from the simulated data.We investigate different methods for effect detection, including univariate and multivariate techniques. Our framework allows us to investigate the complex relationship between sample size, power and effect size for real multivariate data sets. elegans.

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“…This serial framework is quite naturally amenable to recent selective multiple testing methodology proposed by Benjamini and Bogomolov (2014 The contrasts we choose to employ are the periodic B-spline basis functions used to represent the curves (King, Nguyen, and Ionides 2016). Consequently, we base our procedure on the differences in the (i, j)th basis coefficient between the spectral density operator of CAP and TATA, at a given frequency ω.…”

Section: Localizing Differences In Frequency and Along Curvelengthmentioning

confidence: 99%

“…We choose to select significant frequencies and localize the differences between CAP and TATA in a way that controls the expected average of the false discovery proportion over the significant frequencies (Benjamini and Bogomolov 2014). To make this statement precise, let p l = {p(ω l ; i, j) : 1 ≤ i ≤ j ≤ 80} be the set of p-values at frequency ω l , and P = {p 1 , .…”

Section: Localizing Differences In Frequency and Along Curvelengthmentioning

confidence: 99%

Detecting and Localizing Differences in Functional Time Series Dynamics: A Case Study in Molecular Biophysics

Tavakoli

Panaretos

2016

Journal of the American Statistical Association

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Motivated by the problem of inferring the molecular dynamics of DNA in solution, and linking them with its base-pair composition, we consider the problem of comparing the dynamics of functional time series (FTS), and of localizing any inferred differences in frequency and along curvelength. The approach we take is one of Fourier analysis, where the complete second-order structure of the FTS is encoded by its spectral density operator, indexed by frequency and curvelength. The comparison is broken down to a hierarchy of stages: at a global level, we compare the spectral density operators of the two FTS, across frequencies and curvelength, based on a Hilbert-Schmidt criterion; then, we localize any differences to specific frequencies; and, finally, we further localize any differences along the length of the random curves, that is, in physical space. A hierarchical multiple testing approach guarantees control of the averaged false discovery rate over the selected frequencies. In this sense, we are able to attribute any differences to distinct dynamic (frequency) and spatial (curvelength) contributions. Our approach is presented and illustrated by means of a case study in molecular biophysics: how can one use molecular dynamics simulations of short strands of DNA to infer their temporal dynamics at the scaling limit, and probe whether these depend on the sequence encoded in these strands? Supplementary materials for this article are available online.

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Selective Inference on Multiple Families of Hypotheses

Cited by 108 publications

References 26 publications

TreeQTL: hierarchical error control for eQTL findings

TreeQTL: hierarchical error control for eQTL findings

Power Analysis and Sample Size Determination in Metabolic Phenotyping

Detecting and Localizing Differences in Functional Time Series Dynamics: A Case Study in Molecular Biophysics

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