Multi-Scale Models for Non-Stationary Spatial Datasets

This research project will develop statistical methods for spatial data using a model-based approach. The wide availability of location-referenced observations has resulted in a need to analyze and make predictions for very large collections of spatial data. Current models for spatial data have difficulties handling very large numbers of observations irregularly scattered in space.

This project will develop methods for large datasets that contain surfaces with little variability in some parts of the region under study, but high variability in other parts of the region. The statistical methods to be developed will be applicable to the scientific disciplines that use large spatial datasets, including the quantitative environmental sciences, spatial econometrics, and statistical climatology.

In particular, the project will have an impact on the study of essential climate variables that are observed from satellites, such as precipitation, snow cover, and wildfires. The project also will provide an educational and training experience for graduate students. Publicly available software will be developed.

This research project will develop model-based geostatistical methods for non-stationary spatial fields, featuring a multi-resolution structure that is able to capture the variability at different spatial scales. The ability of the model to handle non-stationarity is enhanced by the fact that the resolution changes in space. To achieve scalability to large datasets, the model to be developed will induce sparseness by using compactly supported kernels, coupled with carefully defined prior distributions that introduce strong regularization for the multi-resolution coefficients.

In addition, the model fitting approach developed in this research will avoid costly trans-dimensional Monte Carlo sampling by casting the problem as one of variable selection and Bayesian model averaging. This project will explore two approaches to model fitting. One approach consists of a stochastic search to estimate the non-zero coefficients.

The second approach involves a maximization strategy to estimate the optimal model by applying a regularization term that incorporates information about the structure of a recursive partitioning of the domain. Initially, the model will be developed for Gaussian data. Later, it will be extended for observations in the exponential family of distributions.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.