Research

Publications

Supplementary Material to Publications

Research Statement

My research focuses on statistical models and methods for spatial-temporal processes and their applications to environmental problems. The key problem, in my view, is to find models that allow for interesting spatial-temporal interactions and methods for estimating and assessing the fit of such models. My present focus is on models for Gaussian processes (or processes that can be made Gaussian after a transformation), so that it suffices to specify the mean and covariance structure. The following are the main topics of my personal research;

1. Simply stated, the ultimate goal of any model for space-time covariance functions is to capture the variance of any linear combination of observations of a process accurately. To do this, it is essential to consider the nature of space-time interactions of the process and not just the spatial and temporal variations separately. I have been studying how these interactions relate to the behavior of space-time covariance functions away from the origin and, in turn, how this behavior depends on the space-time spectral density function.
2. Most atmospheric spatial-temporal processes are not time reversible. In particular, the space-time covariance functions are generally not fully symmetric, in that the covariance between site x at time s and site y at time t is not the same as that between x at time s and y at t. Along with doctoral student Mikyoung Jun, I have been developing several approaches to generating space-time covariance functions that are not fully symmetric. Some of the goals of this work are to have flexible and interpretable asymmetries, explicit expressions for the resulting covariance functions, and useful diagnostics for assessing asymmetry.
3. There has been almost no research on covariance structures for space-time processes when the spatial domain is a sphere, despite its obvious relevance to the atmospheric sciences. Along with doctoral student Mikyoung Jun, I have been developing approaches to generate explicit covariance functions for this setting, including ways of producing rich classes of space-time asymmetries.
4. While new and better models are critical to advancing spatial-temporal statistics, one also needs computational and graphical techniques for analyzing and summarizing large space-time datasets. I am currently working on such methods for regularly collected monitoring data, for which a combination of ideas from multiple time series and spatial statistics is appropriate. Models and analyses that work in the spectral domain in time and the spatial domain in space are natural for regular monitoring data and lead to interesting classes of partially nonparametric models that can be fitted reasonably easily using spectral methods.

I am also involved in a number of other research efforts, including:

5. Data assimilation for a sediment transport model in Lake Michigan, with Jon Stroud, Barry Lesht, Dave Schwab and Dmitry Beletsky.
6. Using a physical model for the stratosphere to improve trend estimation of stratospheric ozone, with Serge Guillas and Don Wuebbles.
7. Estimating deformations of isotropic random fields based on a single dense realization, with doctoral student Ethan Anderes.
8. Inferring corrections in emissions inventories from discrepancies in pollution concentrations between monitoring data and a physical model, with Rao Kotamarthi and doctoral student Hae Kyung Im.
9. Modeling the relationship between different versions of a computer model for air pollution, with Jason Ching and doctoral student Xiaofeng Shao.

All of the work described here is supported by CISES (Center for Integrating Statistical and Environmental Statistics), an environmental statistics center funded through the United States EPA STAR program, of which I am currently the director. CISES brings together researchers from many fields to work on a broad array of statistical problems and provides an excellent opportunity for students and postdocs interested in environmental statistics. Downloadable versions of recent papers on some of the topics listed above can be found on the CISES web site.