For stochastic simulation optimization in a modern computing era, we introduce a new parallel framework for solving very large-scale problems using a ranking & selection (R&S) approach that simulates all systems or feasible solutions to provide a global statistical guarantee. We propose a parallel adaptive survivor selection (PASS) framework that...
Cells are often precisely organized into patterns within developing tissues. This precision must emerge from biochemical processes within, and between cells, that are inherently stochastic. I investigated the impact of stochastic gene expression on self-organized pattern formation, focusing on Senseless (Sens), a key target of Wnt and Notch signaling during...
The ever growing desire for accurate estimation and efficient learning necessitates the efforts to quantitatively characterize uncertainties for models. In this thesis, four problems pertaining to uncertainty quantification are discussed: A sequential stopping framework of constructing fixed-precision confidence regions is proposed for a class of multivariate simulation problems where variance...
Forecasting U.S. elections has been a field of interest for many researchers, with various statistical and mathematical models being proposed. In my research, I analyzed a prior election model, the SIS election model. In this model, a system of differential equations traditionally used in epidemiology to study disease transmission (but...