Spring 2021 STAT 30200

Course: STAT 30200

Title: Mathematical Statistics II

Instructor(s): Chao Gao

Course Assistant(s): Wanrong Zhu

Class Schedule: Section 1: TR 2:40 PM-4:00 PM (Remote)

Description: This course continues the development of Mathematical Statistics, with an emphasis on hypothesis testing. Topics include comparison of Bayesian and frequentist hypothesis testing; admissibility of Bayes’ rules; confidence and credible sets; likelihood ratio tests and their asymptotics; Bayes factors; methods for assessing predictions for normal means; shrinkage and thresholding methods; sparsity; shrinkage as an example of empirical Bayes; multiple testing and false discovery rates; Bayesian approach to multiple testing; sparse linear regressions (subset selection and LASSO, proof of estimation errors for LASSO, Bayesian perspective of sparse regressions); and Bayesian model averaging.

Prerequisite(s): STAT 24500 or STAT 30100