Statistical methods

In the medical science, the receiving operationg characteristic (ROC) curve is a graphical representation to evaluate the accuracy of a medical diagnostic test for any cut-off point. The area under the ROC curve (AUC) is an overall performance measure for a diagnostic test. There are two parts in this dissertation. In the first part, we study the properties of bi-Exponentiated Weibull models. FIrst, we derive a general moment formula for single Exponentiated Weibull models. Then we move on to derive the precise formula of AUC and study the maximus likelihood estimation (MLE) of the AUC. Finally, we obtain the asymptotoc distribution of the estimated AUC. Simulation studies are used to check the performance of MLE of AUC under the moderate sample sizes. The second part fo the dissertation is to study the estimation of AUC under the crossing model, which extends the AUC formula in Gonen and Heller (2007).

Understanding where and why organisms are distributed in the environment are central themes in ecology. Animals live in environments in which they are subject to competing demands, such as the need to forage, to find mates, to reproduce, and to avoid predation. Optimal habitats for these various activities are usually distributed heterogeneously in the landscape and may vary both spatially and temporally, causing animals to adjust their locations in space and time to balance these conflicting demands. In this dissertation, I outline three studies of Procambarus fallax in the ridge-slough landscape of Water conservation Area 3A (WCS-3A). The first section outlines an observational sampling study of crayfish population distribution in a four hectare plot, where I statistically model the density distribution at two spatial scales. ... Secondly, I use radio telemetry to study individual adult crayfish movements at two study sites and evaluate habitat selection using Resource Selection Functions. In the third section, I test the habitat selection theory, ideal free distribution, by assessing performance measures (growth and mortality) of crayfish in the two major vegetation types in a late wet season (November 2007) and early wet season (August 2009).

Deterministic and stochastic weighting methods are commonly used methods for estimating missing precipitation rain gauge data based on values recorded at neighboring gauges. However, these spatial interpolation methods seldom check for their ability to preserve site and regional statistics. Such statistics and primarily defined by spatial correlations and other site-to-site statistics in a region. Preservation of site and regional statistics represents a means of assessing the validity of missing precipitation estimates at a site. This study evaluates the efficacy of traditional interpolation methods for estimation of missing data in preserving site and regional statistics. New optimal spatial interpolation methods intended to preserve these statistics are also proposed and evaluated in this study. Rain gauge sites in the state of Kentucky are used as a case study, and several error and performance measures are used to evaluate the trade-offs in accuracy of estimation and preservation of site and regional statistics.

The demand on transportation infrastructure is dramatically increasing due to population growth causing the transportation systems to be pushed to their limits. With the projected population growth, not only for the U.S. but especially for the higher education field, university campuses are of great importance for transportation engineers. Urban univeristy campuses are considered major trip generators and with the population forecast many challenges are bound to arise. The implementation of an improved transit system provides a lower-cost solution to the continuously increasing congestion problems in university campus road networks and surrounding areas. This paper presents a methodology focused on the development of a hybrid system concentrated in three main aspects of transit functionality : access to bus stop location, reasonable travel time and low cost. Two methods for bus stop locations assessment are presented for two levels of analysis : microscopic and mesoscopic. The resulting travel time from the improved bus stop locations is analyzed and compared to the initial conditions by using a microsimulation platform. The development of a mathematical model targets the overall system's cost minimization, including user and operator cost, while maximizing the service coverage. The results demonstrate the benefits of the bus stop assessment by the two applied methods, as well as, the benefits of the route and headway selection based on the mathematical model. Moreover, the results indicate that the generation of routes using travel time as the impedance factor generates the optimal possible routes to obtain the minimum system's overall cost.

The efforts addressed in this thesis refer to assaying the extent of local features in 2D-images for the purpose of recognition and classification. It is based on comparing a test-image against a template in binary format. It is a bioinformatics-inspired approach pursued and presented as deliverables of this thesis as summarized below: 1. By applying the so-called 'Smith-Waterman (SW) local alignment' and 'Needleman-Wunsch (NW) global alignment' approaches of bioinformatics, a test 2D-image in binary format is compared against a reference image so as to recognize the differential features that reside locally in the images being compared 2. SW and NW algorithms based binary comparison involves conversion of one-dimensional sequence alignment procedure (indicated traditionally for molecular sequence comparison adopted in bioinformatics) to 2D-image matrix 3. Relevant algorithms specific to computations are implemented as MatLabTM codes 4. Test-images considered are: Real-world bio-/medical-images, synthetic images, microarrays, biometric finger prints (thumb-impressions) and handwritten signatures. Based on the results, conclusions are enumerated and inferences are made with directions for future studies.

The efforts addressed in this thesis refer to applying nonlinear risk predictive techniques based on logistic regression to medical diagnostic test data. This study is motivated and pursued to address the following: 1. To extend logistic regression model of biostatistics to medical informatics 2. Computational preemptive and predictive testing to determine the probability of occurrence (p) of an event by fitting a data set to a (logit function) logistic curve: Finding upper and lower bounds on p based on stochastical considerations 3. Using the model developed on available (clinical) data to illustrate the bounds-limited performance of the prediction. Relevant analytical methods, computational efforts and simulated results are presented. Using the results compiled, the risk evaluation in medical diagnostics is discussed with real-world examples. Conclusions are enumerated and inferences are made with directions for future studies.

For years attribution research has been dominated by the ANOVA model of behavior which proposes that people construct their dispositional attributions of others by carefully comparing and weighing all situational information using mental computations similar to the processes used by researchers to analyze data. A preliminary experiment successfully determined that participants were able to distinguish differences in variability assessed across persons (high vs. low consensus) and across situations (high vs. low distinctiveness). Also, it was clear that the subjects could evaluate varying levels of situational constraint. A primary experiment administered to participants immediately following the preliminary study determined that participants grossly under-utilized those same variables when making dispositional attributions. Results gave evidence against the use of traditional ANOVA models and support for the use of the Behavior Averaging Principle of Attribution.

Most living organisms transduce electron transport chains in order to obtain energy. Flavin adenine dinucleotide (FAD) is a common electron transfer cofactor found in electron transport proteins referred to as flavoproteins. In this study, the different ionization and oxidation states of this cofactor found in cytochrome b5 reductase were identified spectroscopically and quantified as a function of solution potential and pH. The large data sets obtained from these experiments were analyzed and the acid dissociation constant for reduced cytochrome b5 reductase was determined.

Every day, business owners make important decisions trying to increase productivity. Smaller, family-owned companies, however, have a financial disadvantage over larger corporations. Through the analysis of one small business, Gardens Pool Supply, we provide the owners with answers to questions on how to reduce costs and increase profits.