My research focuses on statistical models and methods for spatial and spatial-temporal processes. In particular, I am interested in the nature of the spatial-temporal interactions implied by these models and on developing statistical methods for assessing these interactions.
My main motivation for studying spatial-temporal processes is to describe variations in the physical environment. In recent years, most of my efforts in this direction relate to problems in climate and weather. Two topics of current interest are methods for combining output from deterministic climate models with observational data to produce realistic spatially and temporally resolved simulations of future temperature and precipitation fields, and ways of estimating temperature extremes that avoid using arbitrary cutoffs for what counts as extreme and that take proper account of seasonality, long-term trends and spatial structure.
Climate datasets (either computer-generated or observational) are generally quite large, leading to two major thrusts of my research. First, when one has lots of spatial-temporal data for the natural environment, it is often apparent that the process is nonstationary in space, time, or both. Thus, the development of nonstationary models plays a central role in my current research. Second, when one has large datasets with complex dependencies, computational issues are critical as they relate to evaluating likelihoods and running simulations. Much of my recent research has considered bringing to bear modern tools from numerical linear algebra to these computational problems.
Other topics of recent research projects include statistical properties of estimates of Gaussian process parameters fitted to deterministic functions and statistical methods for analyzing data from chaotic dynamical systems.