Graduate Students Seminar

Speaker 1: Yewon Kim

Title

An Introduction to Gaussian Graphical Models

Abstract

Wang and Li (2012) proposes a new algorithm for Bayesian model determination in Gaussian Graphical Models (GGM) under G-Wishart prior distributions.  In short, a centered GGM with respect to an undirected graph G is characterized by the parameter set of its precision matrices which is the cone of positive definite matrices with entries corresponding to the missing edges of G constrained to be equal to zero. We first introduce the concept of GGM and review several related papers. Through two data examples, we can investigate the accuracy of the algorithm and understand the network structure.

Speaker 2: Abhishek Balakrishna

Title

Regularity Of The Dirichlet Trace For The Wave Equation With Neumann Boundary Condition

Abstract

We will look at the wave equation on the upper half plane and try to motivate the investigation of the regularity of the Dirichlet and the Neumann trace operators. The traces of the solution are expected to have a certain regularity but a more careful analysis reveals that they possess higher regularity(in space). In particular, the regularity of the Dirichlet trace to the Neumann problem is discussed in detail. We will discuss how microlocal analysis is used to show that for data that is compactly supported away from the boundary, the Dirichlet trace behaves "half better"(regularity wise) in the space variable.