Graduate Student Seminar

Jonathan McHenry

Title

The Proportional Odds Model

Abstract

The proportional odds model is a classic statistical model for data with an ordinal categorical response. Ordinal categorical means that the values are discrete and ordered. The model assumes that the log odds of the cumulative probability for each response category is a linear function of the predictors, with a different intercept for each category but with the same "slope", that is, the same vector of coefficients of the predictors. We collect and examine the mathematical properties of the proportional odds model's likelihood function. We interpret these properties in order to give insight into the applicability of the proportional odds model to data with high dimensional predictors, and to give insight into extensions and generalizations of the model.

Joshua Hudson

Title

The Navier-Stokes equations (a physical derivation)

Abstract

We will go through a heuristic derivation of first Euler's Equation and then the Navier-Stokes equations, illuminating some physical aspects of the equations. We start by defining the convective derivative, and then by using some physical laws applied to a control volume of fluid, we will arrive at a set of partial differential equations which govern the motion of many fluids.