Peter Freeman (Carnegie Mellon University)
Abstract
Textbook approaches to mathematical statistics, the calculus-based course sequence that covers probability and statistical inference concepts, still implicitly revolve around the use of statistical tables and do not effectively utilize computers. In this breakout session, we will present a series of problems that we might expect mathematical statistics students to solve, have attendees discuss standard approaches they might use to solve them now, and demonstrate the computational approaches that we use in our classes for solving them. Our problems will highlight unnecessary transformations and outdated methodologies, and we will show how we replace approaches based on, e.g., large-sample approximations with ones that employ numerical root-finding, simulation, and optimization. Our hope is that session attendees will take away ideas for improving their own mathematical statistics classes (as well as our freely available materials).