Geostatistical Models for the Spatial Distribution of Uranium in the Continental United States

Abstract

Although the United States Geological Survey (USGS) samples geochemical properties across the country, a complete understanding of the distribution of uranium remains elusive. Such an understanding would be useful to many government agencies because uranium can be both harmful to the environment and used to produce nuclear energy. I compare the performance of several nonparametric models for describing the geographic distribution of uranium deposits across the continental United States including the K nearest neighbors method, local regression models, generalized additive models, and Gaussian process models (kriging). I optimize model parameters using cross-validation with a training set and choose the final, most accurate model by comparison of predictions with a test set. I recommend using a kriging model, implemented with lattice krig, and utilizing an optional logarithmic transformation for uranium interpolation. Evidence for successfully avoiding overfitting through this cross-validation process is seen in the applicability of the optimal parameters for the prediction of substances other than uranium.