Department Seminar by Pulong Ma

Please Note: This seminar will be given online.

Gaussian Process Modeling with Applications in Remote Sensing and Coastal Flood Hazard Studies

With space-based observations, remote sensing technology provides a wealth of information for understanding geophysical processes with unprecedented spatial and temporal coverage. Quantitative inference for the global carbon cycle has been bolstered by greenhouse gas observing satellites. NASA’s Orbiting Carbon Observatory-2 (OCO-2) collects tens of thousands of observations of reflected sunlight daily. These observed spectra, or radiances, are used to infer the atmospheric carbon dioxide (CO2) at fine spatial and temporal resolution with substantial coverage across the globe. Remote sensing data processing pipeline involves a series of steps that process the raw instrument data into geophysical variables. Uncertainty quantification (UQ) provides a statistical formalism to understand and characterize uncertainty in this pipeline. Statistical analysis of such data at various levels of processing steps needs to deal with a wide range of challenging problems such as high-dimensionality and nonstationarity. 

In the first part of my talk, I will give an introduction to the OCO-2 mission and science that motivate this research. In the second part of my talk, I will introduce a new family of covariance functions called the Confluent Hypergeometric (CH) class for kriging or Gaussian process modeling, which has been widely used to understand and predict real-world processes.  In the past several decades, the Matérn covariance function has been a popular choice to model dependence structures in spatial statistics. A key benefit of the Matérn class is that it is possible to get precise control over the degree of differentiability of the process realizations. However, the Matérn class possesses exponentially decaying tails, and thus may not be suitable for modeling polynomial-tailed dependence. This problem can be remedied using polynomial covariances; however, one loses control over the degree of differentiability of the process realizations, in that the realizations using polynomial covariances are either infinitely differentiable or not differentiable at all. To overcome this dilemma, a new family of covariance functions is constructed using a scale mixture representation of the Matérn class where one obtains the benefits of both Matérn and polynomial covariances. The resultant covariance contains two parameters: one controls the degree of differentiability near the origin and the other controls the tail heaviness, independently of each other. The CH class also enjoys nice theoretical properties under infill asymptotics including equivalence measures, asymptotic behavior of the maximum likelihood estimators, and asymptotically efficient prediction under misspecified models. The improved theoretical properties in the predictive performance of the CH class are verified via extensive simulations. Application using OCO-2 data confirms the advantage of the CH class over the Matérn class, especially in extrapolative settings. Finally, I will give a brief overview of my research in UQ for remote sensing and coastal flood hazard studies as well as future research directions.