Publication Date

2015

Document Type

Honors Thesis

Department

Mathematics and Statistics

Keywords

Interpolation, Kriging, Geology-Statistical methods, Uranium-Maps, Spatial analysis (Statistics), Spatial interpolation, Local regression, Generalized additive model, Geostatistics

Abstract

Although the United States Geological Survey has been working to sample geochemical properties across the country, a complete understanding of the distribution of uranium in the lower forty-eight states remains elusive. Such an understanding would be useful to many government agencies since uranium can both be harmful to the environment and used to produce nuclear energy. Modeling uranium deposits faces several challenges. First, the samples are not uniformly distributed across the United States, which introduces uncertainty to any model of sparsely sampled areas. Second, standard kriging is not appropriate for this data, since the dis- tribution of uranium is neither symmetric nor normal, and furthermore cannot be easily transformed into a quasi-normal distribution. Third, the large sample size of over 40,000 uranium measurements makes traditional kriging almost impossible on a personal computer. In this thesis, we compare the performance of several non-parametric geostatistical mod- els for uranium deposits. Two classes of models, k nearest neighbors and local regression, make only weak assumptions about the distribution of uranium. Two other classes of mod- els, generalized additive models and kriging-based models, make exible assumptions about the distribution. In the latter case we employ disjunctive kriging, adjusted indicator kriging, and the use of an empirical copula to obtain estimates of uranium that rely minimally on these assumptions. In each case, we tune model parameters using 15-fold cross validation, a procedure which is only feasible through the use of parallel computing techniques. Fur- thermore, evidence for successfully avoiding overfitting through this cross validation is seen in the applicability of our optimal parameters for the prediction of substances other than uranium. We find that although each method produces an interpolation that is visually dis- tinct, the performance of each on the test set, as measured by the root-mean-squared error, is only negligibly different from the others'. We demonstrate dynamic visualizations of these interpolations in Google Earth to better compare and contrast them. We recommend using a Lattice Krig model with an optional logarithmic transformation for uranium interpolation.

Language

English

Comments

164 pages : color illustrations, color maps. Honors project-Smith College, 2015. Includes bibliographical references (pages 157-164)

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