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 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.

To date, most of my methodological work is motivated by applications falling under one of two broad umbrellas. This is in addition of course to some interdisciplinary applications that I find myself working on from time to time. 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). The SIAM/ASA Journal on Uncertainty Quantification defines UQ as “the interface of complex modeling of processes and data, especially characterizations of the uncertainties inherent in the use of such models.” 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.

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. 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.