Mathematics Department

Colloquium

Upcoming Seminar

April 24, 4:10 PM in Physics 123
Noncommutative Fourier analysis of partially ranked data
Luis David Garcia, Department of Mathematics and Statistics, Sam Houston State University

Suppose that you are given the result of a survey in which participants are asked to identify their top $$k$$ choices out of $$n$$ items, e.g., the preferred 3 types of cookies out of 6 Girl Scout cookies. There are several natural summaries of the number counts in this data. For example, we could consider the total number of voters approving of each different $$k$$-subset of the $$n$$ candidates. We could also count the number of voters approving of each individual candidate, or the number of voters approving of each different pair of candidates, or more generally the number of voters approving of each different $$i$$-subset of the $$n$$ candidates. This gives rise to a nested collection of summary statistics that could be used to describe the result of this survey. A natural question to ask is which of these summary statistics best describe the result of our survey? Which statistics capture all the “juice" in the data? About two decades ago, Persi Diaconis proposed using Fourier analysis and algebraic techniques to answer these type of questions for the case of fully ranked data. However, very little is known for the case of partially ranked data. In this talk, we will give an elementary introduction to the Fourier analysis and algebraic techniques involved in the study of both fully and partially ranked data.

Most Thursday afternoons during the academic year, the Reed College Department of Mathematics hosts a math talk. The talks are directed to our mathematics majors but are usually accessible on a variety of levels. Refreshments are served before the talks. For more information, please email davidp at reed.edu.

2013-14 Schedule

Fall

4:10-5:00 in Physics 123 (unless marked otherwise). Directions to Reed.