The increased concentration of greenhouse gases is associated with the global warming in the lower troposphere. For over twenty years, the space physics community has studied a hypothesis of global cooling in the thermosphere, attributable to greenhouse gases. While the global temperature increase in the lower troposphere has been relatively well established, the existence of global changes in the thermosphere is still under investigation. A central difficulty in reaching definite conclusions is the absence of data with sufficiently long temporal and sufficiently broad spatial coverage. Time series of data that cover several decades exist only in a few separated regions. The space physics community has struggled to combine the information contained in these data, and often contradictory conclusions have been reported based on the analyses relying on one or a few locations. To detect global changes in the ionosphere, we present a novel statistical methodology that uses all data, even those with incomplete temporal coverage. It is based on a new functional regression approach that can handle unevenly spaced, partially observed curves. While this research makes a solid contribution to the space physics community, our statistical methodology is very flexible and can be useful in other applied problems.

The estimation of the Pareto distribution can be computationally expensive and the method is badly biased. In this work, an improved Least Squares derivation is used and the estimation will be less biased. Numerical examples and figures are provided so that one may observe the solution more clearly. Furthermore, by varying the different methods of estimation, a comparing of the estimators of the parameters is given. The improved Least Squares derivation is confidently employed for it is economic and efficient.

Sixteen "model building" and "model selection" procedures commonly encountered in industry, all of which were initially alleged to be capable of identifying the best model from the collection of 2k possible linear models corresponding to a given set of k predictors in a multiple linear regression analysis, were individually summarized and subsequently evaluated by considering their comparative advantages and limitations from both a theoretical and a practical standpoint. It was found that none of the proposed procedures were absolutely infallible and that several were actually unsuitable. However, it was also found that most of these techniques could still be profitably employed by the analyst, and specific directional guidelines were recommended for their implementation in a proper analysis. Furthermore, the specific role of the analyst in a multiple linear regression application was clearly defined in a practical sense.

The purpose of this thesis is to analyze various aspects of quality of life and to determine if there is a difference in quality of life offered by a conventional ileostomy versus a continent ileostomy. An instrument was developed to measure several factors thought to influence quality of life as well as several structural/demographic variables. This instrument was designed for persons with a conventional ileostomy and was modified for persons who had undergone conversion surgery from conventional to continent ileostomy. Analysis of variance was performed to determine differences in quality of life for persons with a conventional, conversion, or original continent ileostomy. In addition to an overall quality of life measure, measures for specific areas: self esteem, family relationships, marriage relationships and a composite measure, were tested. No difference was detected for the three types of ileostomy for these variables. Analysis of variance was also performed on variables measuring specific aspects of life such as social activities and travel. This identified several differences in the ileostomy types which the analysis of the more general variables failed to detect. Those who had conversion surgery from conventional to continent ileostomies answered each question twice, comparing life with no ileostomy to life with a conventional, then comparing life with a conventional ileostomy to life with a continent. Three analyses were performed on the resulting data: sign test, chi-square test, and Fisher's exact test. The use of these three tests showed differences in results concerning quality of life and differences in the statistical power of the tests. Both aspects are discussed. Significant improvement in quality of life for almost every aspect tested was seen for this group. Finally, principal component analysis was applied to the set of variables measuring specific aspects of quality of life and several new variables developed from the resulting factors. Analysis of variance was performed on these, as well as the original quality of life measures to determine which of the structural/demographic variables had an effect on quality of life.

Two methods of analyzing multi-dimensional frequency data are detailed. The Second Order Exponential (SOE) model is applicable for dichotomous classifications. The distribution has two sets of parameters, ϴi's and ϴj's. The ϴi's are interpreted as the log of the odds of the marginal probabilities if no two factor relationships exist. Or if all ϴij are not zero, then the ϴi's are analogous to a main effect in a 2m factorial analysis, (m = number of factors or classifications). The ϴif's may be interpreted as a measure and direction of the two factor relationships. These ϴij are analogous to partial or adjusted phi-coefficients. The second method discussed assumes a multinomial distribution and the statistics are developed from an Information Theoretic Approach. Each hypothesis is tested using twice the minimum discrimination information statistic (m.d.i.s), 2I. From the null hypothesis it is possible to estimate unique cell probabilities by an iterative metod. Then 2 is equal to 2 (sample frequencies) log (sample frequencies) - 2 (expected frequencies) log (expected frequencies). (141 pages)

Actigraphy, a technology for measuring a subject's overall activity level almost continuously over time, has gained a lot of momentum over the last few years. An actigraph, a watch-like device that can be attached to the wrist or ankle of a subject, uses an accelerometer to measure human movement every minute or even every 15 seconds. Actigraphy data is often treated as functional data. In this dissertation, we discuss what has been done regarding the visualization of actigraphy data, and then we will explain the three main goals we achieved: (i) develop new multivariate visualization techniques for actigraphy data; (ii) integrate the new and current visualization tools into an R package using object-oriented model design; and (iii) develop an adaptive user-friendly web interface for actigraphy software.

Given the continuing advancement of networking applications and our increased dependence upon software-based systems, there is a pressing need to develop improved security techniques for defending modern information technology (IT) systems from malicious cyber-attacks. Indeed, anyone can be impacted by such activities, including individuals, corporations, and governments. Furthermore, the sustained expansion of the network user base and its associated set of applications is also introducing additional vulnerabilities which can lead to criminal breaches and loss of critical data. As a result, the broader cybersecurity problem area has emerged as a significant concern, with many solution strategies being proposed for both intrusion detection and prevention. Now in general, the cybersecurity dilemma can be treated as a conflict-resolution setup entailing a security system and minimum of two decision agents with competing goals (e.g., the attacker and the defender). Namely, on the one hand, the defender is focused on guaranteeing that the system operates at or above an adequate (specified) level. Conversely, the attacker is focused on trying to interrupt or corrupt the system’s operation. In light of the above, this dissertation introduces novel methodologies to build appropriate strategies for system administrators (defenders). In particular, detailed mathematical models of security systems are developed to analyze overall performance and predict the likely behavior of the key decision makers influencing the protection structure. The initial objective here is to create a reliable intrusion detection mechanism to help identify malicious attacks at a very early stage, i.e., in order to minimize potentially critical consequences and damage to system privacy and stability. Furthermore, another key objective is also to develop effective intrusion prevention (response) mechanisms. Along these lines, a machine learning based solution framework is developed consisting of two modules. Specifically, the first module prepares the system for analysis and detects whether or not there is a cyber-attack. Meanwhile, the second module analyzes the type of the breach and formulates an adequate response. Namely, a decision agent is used in the latter module to investigate the environment and make appropriate decisions in the case of uncertainty. This agent starts by conducting its analysis in a completely unknown milieu but continually learns to adjust its decision making based upon the provided feedback. The overall system is designed to operate in an automated manner without any intervention from administrators or other cybersecurity personnel. Human input is essentially only required to modify some key model (system) parameters and settings. Overall, the framework developed in this dissertation provides a solid foundation from which to develop improved threat detection and protection mechanisms for static setups, with further extensibility for handling streaming data.

The objective of the present study is to investigate key aspects of ovarian and breast cancers, which are two main causes of mortality among women. Identification of the true behavior of survivorship and influential risk factors is essential in designing treatment protocols, increasing disease awareness and preventing possible causes of disease. There is a commonly held belief that African Americans have a higher risk of cancer mortality. We studied racial disparities of women diagnosed with ovarian cancer on overall and disease-free survival and found out that there is no significant difference in the survival experience among the three races: Whites, African Americans and Other races. Tumor sizes at diagnosis among the races were significantly different, as African American women tend to have larger ovarian tumor sizes at the diagnosis. Prognostic models play a major role in health data research. They can be used to estimate adjusted survival probabilities and absolute and relative risks, and to determine significantly contributing risk factors. A prognostic model will be a valuable tool only if it is developed carefully, evaluating the underlying model assumptions and inadequacies and determining if the most relevant model to address the study objectives is selected. In the present study we developed such statistical models for survival data of ovarian and breast cancers. We found that the histology of ovarian cancer had risk ratios that vary over time. We built two types of parametric models to estimate absolute risks and survival probabilities and to adjust the time dependency of the relative risk of Histology. One parametric model is based on classical probability distributions and the other is a more flexible parametric model that estimates the baseline cumulative hazard function using spline functions. In contrast to women diagnosed with ovarian cancer, women with breast cancer showed significantly different survivorship among races where Whites had a poorer overall survival rate compared to African Americans and Other races. In the breast cancer study, we identified that age and progesterone receptor status have time dependent hazard ratios and age and tumor size display non-linear effects on the hazard. We adjusted those non-proportional hazards and non-linear effects by using an extended Cox regression model in order to generate more meaningful interpretations of the data.

The objective of this study is to address some important questions associated with stomach cancer patients using the data from the Surveillance Epidemiology and End Results (SEER) program of the United States. To better understand the behavior of stomach cancer, we first perform parametric analysis for each patient group (white male, white female, African American male, African American female, other male and female) to identify the probability distribution function which can best characterize the behavior of the malignant stomach tumor sizes. We evaluate the effects of patients’ age, gender and race on the malignant stomach tumor sizes by developing quantile regression models, which gives us a better understanding of the behavior of the malignant stomach tumors. We also proposed statistical models with respect to patients’ malignant stomach tumor size as a function of age for different races and gender group, respectively. The proposed models were evaluated to attest their prediction quality. Furthermore, we have identified the rate of change of the malignant tumor size as a function of age, for gender and race. We evaluated the routine treatment of stomach cancer using parametric and nonparametric survival analysis. We have found that stomach cancer patients who receive surgery with radiation together have a better survival probability than the patients who receive only radiation. We performed decision tree analysis to assist the physician in recommending to his patients the most effective treatment that is a function of their characteristics.

Bike Sharing is a sustainable mode of urban mobility, not only for regular commuters but also for casual users and tourists. Free-floating bike sharing (FFBS) is an innovative bike sharing model, which saves on start-up cost, prevents bike theft, and offers significant opportunities for smart management by tracking bikes in real-time with built-in GPS. Efficient management of a FFBS requires: 1) analyzing its mobility patterns and spatio-temporal imbalance of supply and demand of bikes, 2) developing strategies to mitigate such imbalances, and 3) understanding the causes of a bike getting damaged and developing strategies to minimize them. All of these operational management problems are successfully addressed in this dissertation, using tools from Operations Research, Statistical and Machine Learning and using Share-A-Bull Bike FFBS and Divvy station-based bike sharing system as case studies.