Research

I think of myself as an applied Bayesian statistician. I enjoy using sound Bayesian methodology to help scientists and engineers tackle real problems. I believe in allowing the applications to drive the methodology, as opposed to sitting around thinking up some approach for its own sake. In addition to working with other statisticians, I enjoy interdisciplinary collaborations. Such collaborations allow for a healthy exchanges of ideas, and also serve as great exercises in communication since different disciplines seem to have their own languages. Many of us are trying to solve basically the same problems, each from a different perspective. Sharing these perspectives across disciplines can lead to some interesting and useful insights that otherwise would be missed altogether. If you’re interested in collaborating on a project, or if you’re a student looking for a master’s project or a dissertation research topic, feel free to contact me. I’m always interested in exchanging ideas!

To date, most of my work is motivated by applications falling under one of two broad umbrellas. See my publications page or my CV for more details, some preprints, etc.

Uncertainty Quantification

koeqnEngineers and scientists are becoming increasingly reliant on elaborate computational models to study complex physical systems. This is a result of the need to study systems in which collecting real data is extremely difficult due to economic, technical, or ethical limitations, and in which the quantities of interest are unobservable. The utility of such models is contingent upon (i) the models being reasonable surrogates for the systems they are intended to represent, and (ii) all the uncertainties associated with their behavior and predictions being appropriately accounted for when using them to make decisions. Broadly speaking, the study of computer models and statistical approaches to the so-called inverse problem fall under the area of uncertainty quantification (UQ). UQ is a relatively recent interdisciplinary endeavor between engineers, applied mathematicians, and statisticians. A nice trend in UQ from my perspective is the increased interest in Bayesian methodology. This is due in part to the formal incorporation of prior information (e.g., expert opinions, smoothness assumptions on the solutions, etc.) and natural uncertainty quantification (in the form of the posterior distribution) that can be facilitated by the Bayesian approach.

I have ongoing collaborations with both engineers and applied mathematicians where we are interested in using Bayesian methodology to design, validate, and calibrate models of complex systems, as well as to reconstruct regularized solutions to inverse problems with appropriate measures of uncertainty. This has led to some interesting (in my opinion, of course!)  work in computer model calibration where the “right” parameter settings depend on the experimental conditions (so-called state-aware calibration). I also have ongoing work concerning computationally efficient Monte Carlo sampling for, e.g., estimating the posterior distribution of plausible solutions to ill-posed inverse problems, or estimating small probabilities associated with system failures. This research is ongoing; there still remains much interesting work to be done in these avenues.

Neuroimaging   snapshot0001

The collection and analysis of neuroimaging data, most notably magnetic resonance imaging (MRI), has become a widely used technique in the biomedical sciences over the past twenty years or so. Functional MRI (fMRI), as its name implies, is used to study brain function in an effort to identify neural correlates of certain behaviors, as well as to study the causes, symptoms, and treatments of mental illness such as schizophrenia. It’s generally done by observing the blood-oxygenation-level-dependent (BOLD) signal over time,  since this signal is thought to be a good proxy for neuronal activity. Over the past decade, there has been an explosion of interest within the statistics community in fMRI data analysis, resulting in many interesting methods. However, many challenges still remain. My dissertation research involved Bayesian approaches to large-scale inference on functional MRI data while accounting for spatial dependence. Bayesian modeling for fMRI is an issue that I remain interested in. In particular, some things I spend time thinking about include appropriate dependence structures in variable selection models, methods for studying BOLD signal deactivation (in addition to activation), combining fMRI with other imaging modalities for a more complete picture of brain function, and computational approaches to implementing the models we want to use (which is the real bottleneck for any Bayesian working in large-scale settings!).

More recently, I also have become interested in the analysis of structural/clinical MRI data. Structural MRI  is used in clinical settings to study physical characteristics of the brain; e.g., physical changes associated with diseases such as multiple sclerosis or Alzheimer’s disease. Some statistical challenges here involve appropriate methods for quantifying these physical changes over time, identifying the structures of interest in a diseased brain (e.g., segmentation), and relating these characteristics to clinical endpoints.