Graduate Seminar: Kentaro Hoffman, Elyse Borgert
What’s In a Resolution: A Dempster-Schafer approach to Multinomial Hypothesis Tests
Resolution is an omnipresent part of statistical analysis. It comes up in introductory statistics when we are asked if we should treat time as a continuous variable or discrete variable. It comes up when we decide to forecast covid cases with continuous or discrete time models. It even shapes if we view a problem as appropriate for parametric or nonparametric tools. In this talk, we would like to demonstrate how developments in Dempster-Shafer/Fiducial Inference can allow us to make informed decisions about correct resolution choice for Multinomial tests of uniformity.
Persistent topology of protein space
Protein fold classification is a classic problem in structural biology and bioinformatics. We approach this problem using persistent homology. In particular, we use alpha shape filtrations to compare a topological representation of the data with a different representation that makes use of knot-theoretic ideas. We use the statistical method of Angle-based Joint and Individual Variation Explained (AJIVE) to understand similarities and differences between these representations.