My research focuses on inverse problems and uncertainty quantification, incorporating elements of applied and computational mathematics, statistics, and scientific computing.  Broadly speaking, inverse problems involve finding the unknown causes of observed effects, and uncertainty quantification plays a key role in understanding the reliability of predicted effects due to variability in the causes.  In the problems that I consider, these causes are typically the unknown inputs (or parameters) of a system, and the effects are some partial, noisy observations of the system components.  

The main goals of my research are to: (i) design efficient and robust numerical algorithms for system parameter estimation, and (ii) apply these algorithms to analyze real-world data.  My work involves developing sequential algorithms within a Bayesian inference framework to assimilate time series observations, building new mathematical models, and applying sensitivity analysis and parameter identification techniques.  While this work is widely applicable in many fields of science and engineering, much of my focus has been on applications to biology and medicine.  I enjoy working on problems in these areas due to the potential for positive societal impacts in health care as well as the interdisciplinary scientific challenges presented.