My research interests lie in the broad area of statistical computing and modeling. The main theme of my work is the development of computational methods to address inferential problems in statistical modeling. I'm also interested in probabilistic methods for studying these algorithms.
Currently, new models and computational methods are particularly needed when dealing with high-dimensional data as they arise for instance in biomedical and social sciences. I'm interested in models and computational algorithms for dealing with networks in high-dimensional settings.
Another central theme of my research is Monte Carlo methods; particularly methodological and theoretical aspects of Markov Chain Monte Carlo (MCMC). In this area, my interests go in many directions. I'm interested in innovative approaches for combining MCMC and sequential Monte Carlo (SMC) algorithms, and the purpose is mainly for frequentist inference in intractable models. In another direction, I'm interested in understanding the behavior of MCMC algorithms in high-dimensional and infinite dimensional problems.
MCMC is an important tool for carrying inference in many scientific disciplines. For example in psychometrics, Bayesian inference using Markov Chain Monte Carlo is the method of choice for fitting models in item response theory which is currently one of the main approach for educational and psychological assessment. In collaboration with colleagues at the University of Michigan, we are currently working to develop new Monte Carlo algorithms for improved fitting of item response theory models in psychometrics.