# Simple estimators of false discovery rates given as few as one or two p-values without strong parametric assumptions

@inproceedings{Bickel2013SimpleEO, title={Simple estimators of false discovery rates given as few as one or two p-values without strong parametric assumptions}, author={David R. Bickel}, booktitle={Statistical applications in genetics and molecular biology}, year={2013} }

Abstract Multiple comparison procedures that control a family-wise error rate or false discovery rate provide an achieved error rate as the adjusted p-value or q-value for each hypothesis tested. However, since achieved error rates are not understood as probabilities that the null hypotheses are true, empirical Bayes methods have been employed to estimate such posterior probabilities, called local false discovery rates (LFDRs) to emphasize that their priors are unknown and of the frequency type…

## 20 Citations

Small‐scale Inference: Empirical Bayes and Confidence Methods for as Few as a Single Comparison

- Biology
- 2011

Simulations indicate that constrained LFDR MLEs perform markedly better than conventional methods, both in testing and in confidence intervals, for high values of the mixing proportion, but not for low values.

Estimators of the local false discovery rate designed for small numbers of tests

- MathematicsStatistical applications in genetics and molecular biology
- 2012

Corrections of maximum likelihood estimators of the local false discovery rate (LFDR) of histogram-based empirical Bayes methods are introduced and it is found that HBE requires N to be at least 6-12 features to perform as well as the estimators proposed here, with the precise minimum N depending on p0 and dalt.

Empirical Bayes and fiducial effect-size estimation for small numbers of tests

- Mathematics
- 2015

Estimation of an effect size or other parameter of interest (POI), such as an average of differential abundance levels of metabolites or of the differential expression levels of genes, may be…

Empirical Bayes Interval Estimates that are Conditionally Equal to Unadjusted Confidence Intervals or to Default Prior Credibility Intervals

- MathematicsStatistical applications in genetics and molecular biology
- 2012

Two first principles generate both classes of posteriors: a coherence principle and a relevance principle, which means effect size estimates given the truth of an alternative hypothesis cannot depend on whether that truth was known prior to observing the data or whether it was learned from the data.

Null Hypothesis Significance Testing Interpreted and Calibrated by Estimating Probabilities of Sign Errors: A Bayes-Frequentist Continuum

- MathematicsThe American Statistician
- 2020

Abstract Hypothesis tests are conducted not only to determine whether a null hypothesis (H0) is true but also to determine the direction or sign of an effect. A simple estimate of the posterior…

Empirical Bayes estimation of posterior probabilities of enrichment: A comparative study of five estimators of the local false discovery rate

- MathematicsBMC Bioinformatics
- 2011

For enrichment detection, the local FDR is recommended by estimating the LFDR by MLE given at least a medium number of GO terms, by BBE given a small number of Go terms, and by NMLE given either only 1 GO term or precise knowledge of Π0.

A prior-free framework of coherent inference and its derivation of simple shrinkage estimators

- Mathematics
- 2014

A simple yet efficient method of local false discovery rate estimation designed for genome-wide association data analysis

- BiologyStatistical Methods & Applications
- 2021

This work uses the method of moments and introduces a simple, fast and efficient approach for LFDR estimation, assuming a chi-square model with one degree of freedom, which covers many situations in genome-wide association studies.

Blending Bayesian and frequentist methods according to the precision of prior information with applications to hypothesis testing

- MathematicsStat. Methods Appl.
- 2015

The proposed minimax procedure blends strict Bayesian methods with p values and confidence intervals or with default-prior methods. Two applications to hypothesis testing bring some implications to…

A Simple Yet Efficient Parametric Method of Local False Discovery Rate Estimation Designed for Genome-Wide Association Data Analysis

- Biology
- 2019

This work uses the method of moments and introduces a simple, fast and efficient method for LFDR estimation, which is evaluated by analyzing a comprehensive 1000 genomes-based genome-wide association data containing approximately 9.4 million single nucleotide polymorphisms.

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