2008/02/01 by Bradley Efron · 7 citations
Biochemistry, Genetics and Molecular Biology · Decision Sciences · Mathematics · #Gene expression and cancer classification #Psychometric Methodologies and Testing #Statistical Methods in Clinical Trials #stat.ME
paper · pdf · doi:10.1214/07-sts236
published as Statistical Science 2008, Vol. 23, No. 1, 1-22 · This paper commented in: [arXiv:0808.0582], [arXiv:0808.0593], [arXiv:0808.0597], [arXiv:0808.0599]. Rejoinder in [arXiv:0808.0603]. Published in at http://dx.doi.org/10.1214/07-STS236 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2008/02/01 · arxiv created 2008/08/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The classic frequentist theory of hypothesis testing developed by Neyman, Pearson and Fisher has a claim to being the twentieth century’s most influential piece of applied mathematics. Something new is happening in the twenty-first century: high-throughput devices, such as microarrays, routinely require simultaneous hypothesis tests for thousands of individual cases, not at all what the classical theory had in mind. In these situations empirical Bayes information begins to force itself upon frequentists and Bayesians alike. The two-groups model is a simple Bayesian construction that facilitates empirical Bayes analysis. This article concerns the interplay of Bayesian and frequentist ideas in the two-groups setting, with particular attention focused on Benjamini and Hochberg’s False Discovery Rate method. Topics include the choice and meaning of the null hypothesis in large-scale testing situations, power considerations, the limitations of permutation methods, significance testing for groups of cases (such as pathways in microarray studies), correlation effects, multiple confidence intervals and Bayesian competitors to the two-groups model.