Graduate Student Seminar

Speaker 1: Mingkai Yu

Title

Homogenization of a Random walk on a Graph to predict Diffusivity in Obstructed Media

Abstract

We study a particle's random motion in an environment with fine-scale periodic obstructions, for instance, a solute diffusing in a polymer gel.  We model the problem with a continuous time Markov process on an associated periodic, weighted, directed graph where some regions have much faster rates than the other. We show that the random walk, when scaled appropriately, converges to a Brownian motion and its covariance matrix can be computed using graph characteristics. Monte-Carlo simulations are shown to illustrate the limits.

Speaker 2: Zhou Feng

Title

Comparison of Causal Methods for Average Treatment Effect Estimation Allowing Covariate Measurement Error

Abstract

In observational studies, propensity score methods are widely used to estimate average treatment effect (ATE). However, it is common in real world data that a covariate is measured with error, which violate the unconfoundedness assumption. Ignoring measurement error and using naïve propensity scores estimated by observed covariates will lead to biased ATE estimates. There are only a few causal methods that control the influence of covariate measurement error in ATE estimation, and there is no literature comparing their numerical performances. We conduct systematic simulation studies to compare the methods under rationales with respect to Gaussian vs. binary outcome, continuous vs. discrete underlying true covariate, small vs. large treatment effect, and small vs. large measurement error.

The results show that under Gaussian outcome, bias correction method and latent propensity score method using EM algorithm perform best with small and large measurement error respectively; under binary outcome, the inverse probability weighting method and the latent propensity score method using MCMC algorithm perform best with small and large measurement error respectively.