Bayesian Spatial Probit Regression Models and Kernel-Based Space-Time Models: Statistical Methods for Analyzing Land-Atmosphere Interactions

Satellite measurements of Earth's systems enable researchers to study geophysical processes on large spatial scales. One limitation of many of these technologies, however, is cloud cover interference, which create missing values -or "holes"-in derived data products. In studies of land-atmosphere interactions, learning about the missing values may be a primary goal, or an intermediate goal in analyses that require a spatially complete set of observations. In this talk, these goals motivate my presentation of two aspects of my statistical research. First, I present statistical methodology for analyzing spatially-dependent categorical data such as land-cover/land-use observations, where regions are categorized, for example, as either forest, agriculture, urban, or water. In addition to learning about unobserved locations, researchers may want to better understand the economic, geographic, social, and demographic factors that contribute to the land-cover/land-use patterns (e.g., deforestation). When performing such analyses, however, statistical methods must account for spatial dependence. Using a latent variable specification of the Bayesian probit regression model, I show how standard covariance models for spatially-dependent continuous data can be used for discrete response variables. Furthermore, I show how using data augmentation can facilitate faster and more reliable model-fitting algorithms. Second, I present statistical methodology for analyzing space-time transport patterns of satellite-derived measurements of aerosol optical depth over Southeast Asia. Kernel-based methods are often useful in modeling anisotropic and nonstationary space-time data. Within a hierarchical Bayesian framework, the spectral representation of these models has been shown to offer significant computational advantages due to the ability to reduce the dimension of the parameter space. I discuss the ability of these models to capture the complex space-time dynamics of output from MOZART, a global chemistry transport model.