Statistics Seminar – Nikos Ignatiadis (University of Chicago) – Empirical partially Bayes multiple testing and compound chi-square decisions
Feb 13, 2024
3:30PM to 4:30PM
Date(s) - 13/02/2024
3:30 pm - 4:30 pm
Location: KTH B105
Date/Time: Tuesday, February 13, 2024., 3.30 – 4.30 p.m. (will bring refreshments to KTH B105)
Speaker: Nikos Ignatiadis (University of Chicago)
Title: Empirical partially Bayes multiple testing and compound chi-square decisions
Abstract: A common task in high-throughput biology is to screen for associations across thousands of units of interest, e.g., genes or proteins. Often, the data for each unit are modeled as Gaussian measurements with unknown mean and variance and are summarized as per-unit sample averages and sample variances. The downstream goal is multiple testing for the means. In one of the most successful statistical paradigms for this domain, the sample variances are shrunk through empirical Bayes methods before computation of p-values for the means. This situation is thus asymmetric in that a prior is posited and estimated for the nuisance parameters (variances) but not the primary parameters (means). This work initiates the formal study of this paradigm, which we term “empirical partially Bayes multiple testing.” In this framework, if the prior for the variances were known, one could proceed by computing p-values conditional on the sample variances—a strategy called partially Bayes inference by Sir David Cox. We show that these conditional p-values satisfy an Eddington/Tweedie-type formula and are approximated at nearly-parametric rates when the prior is estimated by nonparametric maximum likelihood. If the variances are in fact fixed, the approach retains type-I error guarantees.
Bio: Nikos Ignatiadis is an Assistant Professor of Statistics and Data Science at the University of Chicago. Previously, he was a postdoctoral research scientist at Columbia University and earned a Ph.D. in Statistics from Stanford University in 2022, receiving the Jerome H. Friedman dissertation award for his work. Nikos completed his undergraduate and master’s studies at the University of Heidelberg in Germany, earning degrees in Mathematics, Molecular Biotechnology, and Scientific Computing. His research focuses on developing statistical methods and software for analyzing data from modern technologies, with interests in empirical Bayes analysis, causal inference, and multiple testing.