Statistics, Department of


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A DISSERTATION Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfillment of Requirements For the Degree of Doctor of Philosophy, Major: Statistics, Under the Supervision of Professor David B. Marx. Lincoln, Nebraska: May, 2011

Copyright 2011 Megan Lynne Liedtke Tesar


The overall goal of this research, which is common to most spatial studies, is to predict a value of interest at an unsampled location based on measured values at nearby sampled locations. To accomplish this goal, ordinary kriging can be used to obtain the best linear unbiased predictor. However, there is often a large amount of variability surrounding the measurements of environmental variables, and traditional prediction methods, such as ordinary kriging, do not account for an attribute with more than one level of uncertainty. This dissertation addresses this limitation by introducing a new methodology called weighted kriging. This prediction technique accounts for measurements with significant variability, i.e., soft data, in addition to measurements with little or no variability, i.e., hard data.

To investigate the differences between weighted kriging and ordinary kriging, a simulation study was conducted. Validation statistics were used to evaluate and compare the prediction procedures, and it was found that weighted kriging yields more desirable results than traditional kriging methods. As a follow-up, the prediction procedures were compared using real data from a groundwater quality study.

Bayesian Maximum Entropy (BME) is then introduced as an alternative method to utilize soft data in prediction. Numerical implementation of this approach is possible with the Spatiotemporal Epistemic Knowledge Synthesis-Graphical User Interface (SEKS-GUI). Using this interface, two simulation studies were conducted to investigate the differences between BME and weighted kriging. In the first study, probabilistic soft data in the form of the Gaussian distribution were used. However, since proponents of the BME approach claim that it performs extremely well when the soft data are skewed, the second study used nonsymmetrical soft data generated using a triangular distribution. In both studies, the weighted kriging validation statistics were more desirable than those from BME.

Advisor: David B. Marx