Graduate Students Seminar

Speaker 1: Michael Retzlaff

Title

Mixed Integer PDE-Constrained Optimization for Source Recovery

Abstract

Mixed integer PDE-constrained optimization (MIPEDCO) is a burgeoning field of research which takes the already challenging field of inverse problems bound by partial differential equations, then supplements with the additional constraint that certain variables must maintain integer values.  In this talk, I will describe a typical framework within MIPDECO, then explain its application to a specific problem in source recovery for locating a chemical contaminant or heat source within another medium.  Numerical results will show the paradigm is successful in recovering an approximation to a true source even when only sparse and noisy pointwise measurements are available.  Lastly, I will discuss ongoing work, which is to reduce the large computational cost associated with finding the numerical solutions.

Speaker 2: Abhishek Guin

Title

Bayesian Analysis of Singly Imputed Synthetic Data under the Multiple Linear Regression Model

Abstract

We will discuss how to perform Bayesian inference based on singly imputed partially synthetic data, when the original data follow a multiple linear regression model. We consider two methods of synthetic data generation: plug-in sampling, where unknown parameters in the data model are set equal to observed values of their point estimators based on the original data, and synthetic data are drawn from this estimated version of the model; and posterior predictive sampling, where the imputer assumes a prior on the unknown parameters, and synthetic data are drawn from this imputed posterior version of the model.