Winter 2024 STAT 27855-1

Course: STAT 27855

Title: Hypothesis Testing with Empirical Bayes Methodology

Instructor(s): Daniel Xiang

Teaching Assistant(s): TBA

Class Schedule: Sec 1: TR 12:30 PM-1:50 PM in Ryerson 178

Description: Large scale data sets regularly produced in fields such as biology, social sciences, and neuroscience bring new challenges, like controlling the amount of false positives when testing many hypotheses, as well as the opportunity to leverage information across the entire dataset toward making individual inferences. In this course, we will study theoretical foundations and practical aspects of hypothesis testing in a Bayesian framework. We will focus attention on the local false discovery rate (lfdr), which represents the probability that the null hypothesis is true given the data, and learn several methods for estimating this quantity. Decision theory provides a formal connection between quantities of interest in a Bayesian framework to population parameters in a strictly frequentist model, where the truth status of each null hypothesis is fixed and unknown. We may also discuss methodology for estimating the null distribution, and methods for finite-sample lfdr control if time permits. Homework assignments will have theoretical and computational components.