Ecological problems often require multivariate analyses. Ever since Bray and Curtis (1957) drew an analogy between Euclidean distance and community dissimilarity, most multivariate ecological inference has been based on geometric ideas. For example, ecologists routinely use distance-based ordination methods (e.g. multidimensional scaling) to enhance the interpretability of multivariate data. More recently, distance-based diversity indices that account for functional differences between species are now routinely used. But in most other areas of science, inference is based on Fisher's (1922) likelihood concept; statisticians view likelihood as an advance over purely geometric approaches. Nevertheless, likelihood-based reasoning is rare in multivariate statistical ecology. Using ordination and functional diversity as case studies, my thesis addresses the questions: Why is likelihood rare in multivariate statistical ecology? Can likelihood be of practical use in multivariate analyses of real ecological data? Should the likelihood concept replace multidimensional geometry as the foundation for multivariate statistical ecology? I trace the history of quantitative plant ecology to argue that the geometric focus of contemporary multivariate statistical ecology is a legacy of an early 20th century debate on the nature of plant communities. Using the Rao-Blackwell and Lehmann-Scheffé theorems, which both depend on the likelihood concept, I show how to reduce bias and sampling variability in estimators of functional diversity. I also show how to use likelihood-based information criteria to select among ordination methods. Using computationally intensive Markov-chain Monte Carlo methods, I demonstrate how to expand the range of likelihood-based ordination procedures that are computationally feasible. Finally, using philosophical ideas from formal measurement theory, I argue that a likelihood-based multivariate statistical ecology outperforms the geometry-based alternative by providing a stronger connection between analysis and the real world. Likelihood should be used more often in multivariate ecology.

Multivariate statistics play an important role in performance analysis of wireless communication systems in correlated fading channels. This thesis presents a framework which can be used to derive easily computable mathematical representations for some multivariate statistical distributions, which are derivatives of the Gaussian distribution, and which have a particular correlation structure. The new multivariate distribution representations are given as single integral solutions of familiar mathematical functions which can be evaluated using common mathematical software packages. The new approach can be used to obtain single integral representations for the multivariate probability density function, cumulative distribution function, and joint moments of some widely used statistical distributions in wireless communication theory, under an assumed correlation structure. The remarkable advantage of the new representation is that the computational burden remains at numerical evaluation of a single integral, for a distribution with an arbitrary number of dimensions. The new representations are used to evaluate the performance of diversity combining schemes and multiple input multiple output systems, operating in correlated fading channels. The new framework gives some insights into some long existing open problems in multivariate statistical distributions. / Communications

This dissertation develops a set of nonlinear variation pattern identification methods that are intended to aid in diagnosing the root causes of product variability in complex manufacturing processes, in which large amounts of high dimensional in-process measurement data are collected for quality control purposes. First, a nonlinear variation pattern model is presented to generically represent a single nonlinear variation pattern that results from a single underlying root cause, the nature of which is unknown a priori. We propose a modified version of a principal curve estimation algorithm for identifying the variation pattern. Principal curve analysis is a nonlinear generalization of principal components analysis (PCA) that lends itself well to interpretation and also has theoretically rich underpinnings. The principal curve modification involves a dimensionality reduction step that is intended to improve estimation accuracy by reducing noise and improving the robustness of the algorithm with the high-dimensional data typically encountered in manufacturing. An effective visualization technique is also developed to help interpret the identified nonlinear variation pattern and aid in root cause identification and elimination. To further improve estimation robustness and accuracy and reduce computational expense, we propose a local PCA based polygonal line algorithm to identify the nonlinear patterns. We also develop an approach for separating and identifying the effects of multiple nonlinear variation patterns that are present simultaneously in the measurement data. This approach utilizes higher order cumulants and pairwise distance based clustering to separate the patterns and borrows from techniques that are used in linear blind source separation. With the groundwork laid for a versatile flexible and powerful nonlinear variation pattern modeling and identification framework, applications in autobody assembly and stamping processes are investigated. The pattern identification algorithms, together with the proposed visualization approach, provides an effective tool to aid in understanding the nature of the root causes of variation that affect a manufacturing process.

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Ecological problems often require multivariate analyses. Ever since Bray and Curtis (1957) drew an analogy between Euclidean distance and community dissimilarity, most multivariate ecological inference has been based on geometric ideas. For example, ecologists routinely use distance-based ordination methods (e.g. multidimensional scaling) to enhance the interpretability of multivariate data. More recently, distance-based diversity indices that account for functional differences between species are now routinely used. But in most other areas of science, inference is based on Fisher's (1922) likelihood concept; statisticians view likelihood as an advance over purely geometric approaches. Nevertheless, likelihood-based reasoning is rare in multivariate statistical ecology. Using ordination and functional diversity as case studies, my thesis addresses the questions: Why is likelihood rare in multivariate statistical ecology? Can likelihood be of practical use in multivariate analyses of real ecological data? Should the likelihood concept replace multidimensional geometry as the foundation for multivariate statistical ecology? I trace the history of quantitative plant ecology to argue that the geometric focus of contemporary multivariate statistical ecology is a legacy of an early 20th century debate on the nature of plant communities. Using the Rao-Blackwell and Lehmann-Scheffé theorems, which both depend on the likelihood concept, I show how to reduce bias and sampling variability in estimators of functional diversity. I also show how to use likelihood-based information criteria to select among ordination methods. Using computationally intensive Markov-chain Monte Carlo methods, I demonstrate how to expand the range of likelihood-based ordination procedures that are computationally feasible. Finally, using philosophical ideas from formal measurement theory, I argue that a likelihood-based multivariate statistical ecology outperforms the geometry-based alternative by providing a stronger connection between analysis and the real world. Likelihood should be used more often in multivariate ecology.

Ultrasonic testing is a nondestructive structural characterization technique with limited examples of application for polymeric products due to the high signal attenuation in this class of materials. Recent developments in this thesis on ultrasonics have focused on a guided waves test method and used nonlinear analysis of harmonic frequencies to characterize polyethylene, a semi-crystalline polymer. This sensor technology was demonstrated in the detection of initial plastic deformation and to monitor solvent swelling. Frequency regions of low signal attenuation and a nonlinear ultrasonic parameter using amplitude ratio of harmonic peaks were used to classify different crystalline morphologies, controlled by thermal treatment. With an established connection between the ultrasonic spectrum signal and the internal structure of polyethylene, a quality monitoring tool was developed and applied to a batch rotational molding process. Multiple traditional quality measurements were correlated with the ultrasonic signal using multivariate statistical analysis. Finally, an in-line statistical approach for quality classification and an on-line process monitoring using dynamic process modeling were validated. The results presented in this study demonstrate the relevancy of incorporation of the ultrasonic sensor technology to promote advanced manufacturing practices for the polymer manufacturing industry. / Thesis / Doctor of Philosophy (PhD) / We have been using ultrasonic devices to investigate different things from medical diagnosis of prenatal development to nondestructive exploration of small rocks brought from the Moon. This study takes the ultrasonic testing to the challenge of characterizing plastics. Using information from the propagation of these inaudible sound waves, we can explore the entire structure and observe structural changes that can lead to defects or failures. With the help of computer-based data processing, we investigate these complex signals creating tools for more efficient manufacturing and safer products like water and fuel storage tanks.

In this work, an automated statistical approach for the condition monitoring of a fluid power system based on a process sensor network is presented. In a multistep process, raw sensor data are processed by feature extraction, selection and dimensional reduction and finally mapped to discriminant functions which allow the detection and quantification of fault conditions. Experimentally obtained training data are used to evaluate the impact of temperature and different aeration levels of the hydraulic fluid on the detection of pump leakage and a degraded directional valve switching behavior. Furthermore, a robust detection of the loading state of the installed filter element and an estimation of the particle contamination level is proposed based on the same analysis concept.

The ground water quality of the Trinity Aquifer for wells sampled between 2000 and 2009 was examined using multivariate and spatial statistical techniques. A Kruskal-Wallis test revealed that all of the water quality parameters with the exception of nitrate vary with land use. A Spearman’s rho analysis illustrates that every water quality parameter with the exception of silica correlated with well depth. Factor analysis identified four factors contributable to hydrochemical processes, electrical conductivity, alkalinity, and the dissolution of parent rock material into the ground water. The cluster analysis generated seven clusters. A chi-squared analysis shows that Clusters 1, 2, 5, and 6 are reflective of the distribution of the entire dataset when looking specifically at land use categories. The nearest neighbor analysis revealed clustered, dispersed, and random patterns depending upon the entity being examined. The spatial autocorrelation technique used on the water quality parameters for the entire dataset identified that all of the parameters are random with the exception of pH which was found to be spatially clustered. The combination of the multivariate and spatial techniques together identified influences on the Trinity Aquifer including hydrochemical processes, agricultural activities, recharge, and land use. In addition, the techniques aided in identifying areas warranting future monitoring which are located in the western and southwestern parts of the aquifer.

Due to the eminent shortage of 3He, there exists a significant need to develop a new (or optimize an existing) neutron detection system which would reduce the dependency on the current 3He-based detectors for Domestic Nuclear Detection Office (DNDO) applications. The purpose of this research is to develop a novel methodology for optimizing candidate neutron detector designs using multivariate statistical analysis of Monte Carlo radiation transport code (MCNPX) models. The developed methodology allows the simultaneous optimization of multiple detector parameters with respect to multiple response parameters which measure the overall performance of a candidate neutron detector. This is achieved by applying three statistical strategies in a sequential manner (namely factorial design experiments, response surface methodology, and constrained multivariate optimization) to results generated from MCNPX calculations. Additionally, for organic scintillators, a methodology incorporating the light yield non-proportionality is developed for inclusion into the simulated pulse height spectra (PHS). A Matlab® program was developed to post-process the MCNPX standard and PTRAC output files to automate the process of generating the PHS thus allowing the inclusion of nonlinear light yield equations (Birks equations) into the simulation of the PHS for organic scintillators. The functionality of the developed methodology is demonstrated on the successful multivariate optimization of three neutron detection systems which utilize varied approaches to satisfying the DNDO criteria for an acceptable alternative neutron detector. The first neutron detection system optimized is a 3He-based radiation portal monitor (RPM) based on a generalized version of a currently deployed system. The second system optimized is a 6Li-loaded polymer composite scintillator in the form of a thin film. The final system optimized is a 10B-based plastic scintillator sandwiched between two standard plastic scintillators. Results from the multivariate optimization analysis include not only the identification of which factors significantly affect detector performance, but also the determination of optimum levels for those factors with simultaneous consideration of multiple detector performance responses. Based on the demonstrated functionality of the developed multivariate optimization methodology, application of the methodology in the development process of new candidate neutron detector designs is warranted.

Gilles de la Tourette syndrome (GTS) is a chronic neuropsychiatric disorder characterized by multiple motor and vocal tics, affecting approximately 1% of the population. The precise neuropathology of GTS has not yet been delineated, but current models implicate subcortical and cortical areas - the cortico-striato-thalamo-cortical (CSTC) circuit. The majority of studies in the literature have either dealt with GTS with comorbid conditions and/or children with GTS. As these factors are known to affect brain structure and function, it unknown what the neurobiological underpinnings of pure adult GTS are. The objective of this body of work was to use functional magnetic resonance imaging (fMRI) and diffusion tensor imaging (DTI) to characterize differences in brain function and structure in pure adult GTS patients versus age- and sex-matched controls. I employed a series of three distinct analyses for this purpose, based upon current models of CSTC circuit-related dysfunction in GTS. In the first, GTS patients and control participants executed three finger-tapping paradigms that varied in both complexity and memory requirements. These finger-tapping tasks were modeled after previous studies that showed CSTC circuit-related activity in healthy individuals. Using a multivariate statistical technique to assess task-related patterns of activation across the whole brain, I found that, while there was much overlap in brain activation patterns between groups, sensorimotor cortical regions were differentially recruited by GTS patients compared to controls. In the second fMRI analysis, I measured low-frequency spontaneous fluctuations of the blood oxygen level dependent signal during rest, and found that GTS patients exhibited greater resting state functional connectivity with the left putamen compared to controls. In the final analysis, DTI was used to provide a whole-brain assessment of regional diffusion anisotropy in GTS patients and healthy volunteers and to investigate the fractional anisotropy in predetermined ROIs. This analysis found no differences between GTS patients and controls. Overall, my findings indicated that several CSTC-related regions shown to be atypical in GTS patients previously, are also atypical in pure adult GTS, and that sensorimotor cortical regions and the putamen may be regions of functional disturbance in pure adult GTS.