Graduate Thesis Or Dissertation

Tools for environmental statistics : creative visualization and estimating variance from complex surveys

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  • Environmental monitoring poses two challenges to statistical analysis: complex data and complex survey designs. Monitoring for system health involves measuring physical, chemical, and biological properties that have complex relations. Exploring these relations is an integral part of understanding how systems are changing under stress. How does one explore high dimensional data? Many of our current methods rely on "black-box" mathematical methods. Visualization techniques on the other hand are either restricted to low dimensions or hopelessly out of context. The first topic explored in this dissertation suggests a direct search method for use in projection pursuit guided tours. In Chapter 2 a direct search method for index optimization, the multidirectional pattern search, was explored for use in projection pursuit guided tours. The benefit of this method is that it does not require the projection pursuit index to be continuously differentiable; in contrast to existing methods that require differentiability. Computational comparisons with test data revealed the feasibility and promise of the method. It successfully found hidden structure in 4 of 6 test data sets. The study demonstrates that the direct search method lends itself well to use in guided tours and allows for non-differentiable indices. Evaluating estimators of the population variance is covered in Chapter 3. Good estimates of the population variance are useful when designing a survey. These estimates may come from a pilot project or survey. Often in environmental sampling simple random sampling is not possible;· instead complex designs are used. In this case there is no clear estimator for the population variance. We propose an estimator that is (1) based on a methods of moments approach and (2) extendible to more complex variance component models. Several other estimators have been proposed in the literature. This study compared our method of moment estimator to other variance estimators. Unfortunately our estimator did not do as well as some of the other estimators that have been suggested implying that these estimators do not perform similarly as the literature suggests they do. Two estimators, the sample variance and a ratio estimator based on the Horvitz-Thompson Theorem and a consistency argument, proved to be favorable.
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