This page should give you an idea of what topics of Statistics and Data Science are of particular interest to me currently. For more details on current projects my students and I are involved in, check out the Current Projects page.
Development of new Statistics and Data Science Methodology, Algorithms, Theory and Software (MATS) : As with most researchers in our discipline, the only reason I am in this job is because I enjoy discovering and developing new statistical and data science techniques, devising algorithms for implementing such techniques, (very importantly for me) developing mathematical and theoretical machinery to understand why, where, when and how such new methods work, and eventually writing software on such methods for use by others.
I prefer working with what I call conditional statistical procedures, where the inference, prediction and decision-making process is conditional on the observed data. This includes resampling techniques and Bayesian statistics , which is what I work on currently. Soon, I should be able to include empirical likelihood to this list, hopefully.
The approach that my students and I take is to start with a real-world application that is of interest to us. Currently, these applications are from (i) remote sensing and earth sciences, (ii) socio-economic-political sciences, (iii) neuroscience and imaging. Open questions from these sciences are framed in terms of Statistics and Data Science challenges, which leads us to the MATS development process described above.
Most datasets from the above applications are big data, with spatio-temporal and other complex dependencies, consequently, our MATS development process accounts for both big data features, and various kinds of observable, hierarchical, or latent dependencies. One approach that we adopt, which I believe is quite unique, is to study the geometry of high-dimensional, dependent data. Other techniques we use include modeling using functional and non-parametric components, change detection, dimension reduction, sparsity, model selection and averaging, hierarchical modeling. Caveat: we do asymptotics (often), and correctly (always)!