My research investigates problems arising in identification and control of stochastic systems. Recently, I have worked on algorithms for identifying and tracking the time-varying parameters of a linear system whose coefficients evolve as a slowly-varying Markov chain. I also recently worked on a two-phase procedure for estimation and noise attenuation in systems with unmodeled dynamics and stochastic signal errors. Additionally, in a joint effort with the US Air Force Research Labs, I am investigating methods for cooperative navigation of Unmanned Aerial Vehicles without the use of GPS.I also work on problems in applications and have recently began some projects attempting to use Topological Data Analysis on data sets to reveal information classical statistics may obfuscate.
My current research effort is trying to develop stronger mathematical foundations for uncertainty quantification related to problems in materials design. One example of a problem I'm working on is the simulation and analysis of stiff chemical reaction networks. This can be modeled as a high dimensional Markov chain, and much has been done to heuristically use averaging principles to simulate the evolution of the system. I am working on some more rigorous formulations of the problem to derive better insights and methods for simulation and analysis.
See the following list of projects and talks I've given relating statistics and stochastic systems to applied problems.