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Congestion on roadways and high level of uncertainty of traffic conditions are major considerations for trip planning. The purpose of this research is to investigate the characteristics and patterns of spatial and temporal correlations and also to detect other variables that affect correlation in a freeway setting. 5-minute speed aggregates from the Performance Measurement System (PeMS) database are obtained for two directions of an urban freeway – I-10 between Santa Monica and Los Angeles, California. Observations are for all non-holiday weekdays between January 1st and June 30th, 2010. Other variables include traffic flow, ramp locations, number of lanes and the level of congestion at each detector station. A weighted least squares multilinear regression model is fitted to the data; the dependent variable is Fisher Z transform of correlation coefficient. Estimated coefficients of the general regression model indicate that increasing spatial and temporal distances reduces correlations. The positive parameters of spatial and temporal distance interaction term show that the reduction rate diminishes with spatial or temporal distance. Higher congestion tends to retain higher expected value of correlation; corrections to the model due to variations in road geometry tend to be minor. The general model provides a framework for building a family of more responsive and better-fitting models for a 6.5 mile segment of the freeway during three times of day: morning, midday, and afternoon. Each model is cross-validated on two locations: the opposite direction of the freeway, and a different location on the direction used for estimation. Cross-validation results show that models are able to retain 75% or more of their original predictive capability on independent samples. Incorporation of predictor variables that describe road geometry and traffic conditions into the model works beneficially in capturing a significant portion of variance of the response. The developed regression models are thus transferrable and are apt to predict correlation on other freeway locations.

This research uses satellite data and the moment statistics to determine if solar farms can be placed in the Southeast US. From 2001-2019, the data are analyzed in reference to the Southwest US, where solar farms are located. The clean energy need is becoming more common; therefore, more locations than arid environments must be observed. The Southeast US is the main location of interest due to the warm, moist environment throughout the year. This research uses the Global Land Surface Satellite (GLASS) photosynthetically active radiation product (PAR) to determine viable locations for solar panels. A probability density function (PDF) along with the moment statistics are utilized to determine statistic thresholds from solar farms in the Southwest US. For the Southeast US, three major locations were determined to be a viable option: Mississippi Delta, Northwest Florida, and Southwestern Alabama. This research shows that solar farms can be efficient in areas with more convective cloud cover, such as the Southeast US.

The Mississippi River Valley Alluvial Aquifer (MRVAA) is one of the most productive agricultural regions in the United States. The main objectives of this research are to identify long term trends and change points in hydrological variables (streamflow and rainfall), to assess the relationship between hydrological variables, and to evaluate the influence of global climate indices on hydrological variables. Non-parametric tests, MMK and Pettitt’s tests were used to analyze trend and change points. PCC and Streamflow elasticity analysis were used to analyze the relationship between streamflow and rainfall and the sensitivity of streamflow to rainfall changes. PCC and MLR analysis were used to evaluate the relationship between climate indices and hydrological variables and the combined effect of climate indices with hydrological variables. The results of the trend analysis indicated spatial variability within the aquifer, increase in streamflow and rainfall in the Northern region of the aquifer, while a decrease was observed in the southern region of the aquifer. Change point analysis of annual maximum, annual mean streamflow and annual precipitation revealed that statistically decreasing shifts occurred in 2001, 1998 and 1995, respectively. Results of PCC analysis indicated that streamflow and rainfall has a strong positive relationship between them with PCC values more than 0.6 in most of the locations within the basin. Results of the streamflow elasticity for the locations ranged from 0.987 to 2.33 for the various locations in the basin. Results of the PCC analysis for monthly maximum and mean streamflow showed significant maximum positive correlation coefficient for Nino 3.4. Monthly maximum rainfall showed a maximum significant positive correlation coefficient for PNA and Nino3.4 and the monthly mean rainfall showed a maximum significant positive correlation coefficient of 0.18 for Nino3.4. Results of the MLR analysis showed a maximum significant positive correlation coefficient of 0.31 for monthly maximum and mean streamflow of 0.21 and 0.23 for monthly maximum and mean rainfall, respectively. Overall, results from this research will help in understanding the impacts of global climate indices on rainfall and subsequently on streamflow discharge, so as to mitigate and manage water resource availability in the MRVAA underlying the LMRB.

The transition of natural landscapes to intensive agricultural uses has resulted in severe loss of soil organic carbon (SOC), increased CO₂ emissions, river depletion, and groundwater overdraft. Despite negative documented effects of agricultural land use (i.e., soil erosion, nutrient runoff) on critical natural resources (i.e., water, soil), food production must increase to meet the demands of a rising human population. Given the environmental and agricultural productivity concerns of intensely managed soils, it is critical to implement conservation practices that mitigate the negative effects of crop production and enhance environmental integrity. In the Mississippi Alluvial Valley (MAV) region of Mississippi, USA, the adoption of cover crop (CC) and no-tillage (NT) management practices has been low because of a lack of research specific to the regional nuances. Therefore, this study assessed the long-term soil physiochemical and biological responses from integrating CC and NT management to agricultural soils of the region. Research plots were established in a split-block design with two tillage treatments: NT and reduced tillage (RT) and three CC treatments: no cover (NC), rye (RY) and a rye+clover (RC) mix. Soil samples were taken during the growing season of 2019 and 2020. Bulk density was found to be significantly lower in NT plots and aggregate stability was greatest in plots with a single CC species. Moisture retention increased in NT.. Soil organic carbon was greater in NT and CC treatments and there was no difference in CO₂ flux. Bacterial abundance had a positive effect on SOC but a negative effect on CO₂. The rate of proportional change and pattern of variability in C pools suggested loss of SOC in reduced tillage (RT) treatments. Microbial abundance, functional genes and enzyme activity was greater in NT with CC, but diversity was greater in RT. No-tillage practices lower diversity and influence long-term community changes while CC practices enact a seasonal response to environmental conditions. I conclude that in heavy clay soils of the mid-South region of the MAV, RT with a CC is optimal for soil health traits associated with crop sustainability, however the management will still contribute to increased CO₂ emissions.

<p>This dissertation address two significant challenges in the causal inference workflow for Big Observational Data. The first is designing Big Observational Data with high-dimensional and heterogeneous covariates. The second is performing uncertainty quantification for estimates of causal estimands that are obtained from the application of black box machine learning algorithms on the designed Big Observational Data. The methodologies developed by addressing these challenges are applied for the design and analysis of Big Observational Data from a large public university in the United States. </p> <h4>Distributed Design</h4> <p>A fundamental issue in causal inference for Big Observational Data is confounding due to covariate imbalances between treatment groups. This can be addressed by designing the study prior to analysis. The design ensures that subjects in the different treatment groups that have comparable covariates are subclassified or matched together. Analyzing such a designed study helps to reduce biases arising from the confounding of covariates with treatment. Existing design methods, developed for traditional observational studies consisting of a single designer, can yield unsatisfactory designs with sub-optimum covariate balance for Big Observational Data due to their inability to accommodate the massive dimensionality, heterogeneity, and volume of the Big Data. We propose a new framework for the distributed design of Big Observational Data amongst collaborative designers. Our framework first assigns subsets of the high-dimensional and heterogeneous covariates to multiple designers. The designers then summarize their covariates into lower-dimensional quantities, share their summaries with the others, and design the study in parallel based on their assigned covariates and the summaries they receive. The final design is selected by comparing balance measures for all covariates across the candidates and identifying the best amongst the candidates. We perform simulation studies and analyze datasets from the 2016 Atlantic Causal Inference Conference Data Challenge to demonstrate the flexibility and power of our framework for constructing designs with good covariate balance from Big Observational Data.</p> <h4>Designed Bootstrap</h4> <p>The combination of modern machine learning algorithms with the nonparametric bootstrap can enable effective predictions and inferences on Big Observational Data. An increasingly prominent and critical objective in such analyses is to draw causal inferences from the Big Observational Data. A fundamental step in addressing this objective is to design the observational study prior to the application of machine learning algorithms. However, the application of the traditional nonparametric bootstrap on Big Observational Data requires excessive computational efforts. This is because every bootstrap sample would need to be re-designed under the traditional approach, which can be prohibitive in practice. We propose a design-based bootstrap for deriving causal inferences with reduced bias from the application of machine learning algorithms on Big Observational Data. Our bootstrap procedure operates by resampling from the original designed observational study. It eliminates the need for additional, costly design steps on each bootstrap sample that are performed under the standard nonparametric bootstrap. We demonstrate the computational efficiency of this procedure compared to the traditional nonparametric bootstrap, and its equivalency in terms of confidence interval coverage rates for the average treatment effects, by means of simulation studies and a real-life case study.</p> <h4>Case Study</h4> <p>We apply the distributed design and designed bootstrap methodologies in a case study involving institutional data from a large public university in the United States. The institutional data contains comprehensive information about the undergraduate students in the university, ranging from their academic records to on-campus activities. We study the causal effects of undergraduate students’ attempted course load on their academic performance based on a selection of covariates from these data. Ultimately, our real-life case study demonstrates how our methodologies enable researchers to effectively use straightforward design procedures to obtain valid causal inferences with reduced computational efforts from the application of machine learning algorithms on Big Observational Data.</p> <p><br></p>

In this paper, I analyze the effectiveness of state level Earned Income Tax Credit programs on improving of poverty levels. I conducted this analysis for the years 1991 through 2011 using a panel data model with fixed effects. The main independent variables of interest were the state and federal EITC rates, minimum wage, gross state product, population, and unemployment all by state. I determined increases to the state EITC rates provided only a slight decrease to both the overall white below-poverty population and the corresponding white childhood population under 18, while both the overall and the under-18 black population for this category realized moderate decreases in their poverty rates for the same time period. I also provide a comparison of the effectiveness of the state level EITCs and minimum wage at the state level over the same time period on these select demographic groups.

Abstract The Atlantic Sturgeon (Acipenser oxyrinchus oxyrinchus, Mitchell) is an anadromous species that spawns in tidal freshwater rivers from Canada to Florida. Overfishing, river sedimentation and alteration of the river bottom have decreased Atlantic Sturgeon populations, and NOAA lists the species as endangered. Ecologists sometimes find it difficult to locate individuals of a species that is rare, endangered or invasive. The need for methods less invasive that can create more resolution of cryptic species presence is necessary. Environmental DNA (eDNA) is a non-invasive means of detecting rare, endangered, or invasive species by isolating nuclear or mitochondrial DNA (mtDNA) from the water column. We evaluated the potential of eDNA to document the presence of Atlantic Sturgeon in the James River, Virginia. Genetic primers targeted the mitochondrial Cytochrome Oxydase I gene, and a restriction enzyme assay (DraIII) was developed. Positive control mesocosm and James River samples revealed a nonspecific sequence—mostly bacteria commonly seen in environmental waters. Methods more stringent to a single species was necessary. Novel qPCR primers were derived from a second region of Cytochrome Oxydase II, and subject to quantitative PCR. This technique correctly identified Atlantic Sturgeon DNA and differentiated among other fish taxa commonly occurring in the lower James River, Virginia. Quantitative PCR had a biomass detection limit of 32.3 ug/L and subsequent analysis of catchment of Atlantic Sturgeon from the Lower James River, Virginia from the fall of 2013 provided estimates of 264.2 ug/L Atlantic Sturgeon biomass. Quantitative PCR sensitivity analysis and incorporation of studies of the hydrology of the James River should be done to further define habitat utilization by local Atlantic Sturgeon populations. IACUC: AD20127

Analyzing the structure of a dataset is a challenging problem in high-dimensions as the volume of the space increases at an exponential rate and typically, data becomes sparse in this high-dimensional space. This poses a significant challenge to machine learning methods which rely on exploiting structures underlying data to make meaningful inferences. This dissertation proposes the <i>n</i>-TARP method as a building block for high-dimensional data analysis, in both supervised and unsupervised scenarios.<div><br></div><div>The basic element, <i>n</i>-TARP, consists of a random projection framework to transform high-dimensional data to one-dimensional data in a manner that yields point separations in the projected space. The point separation can be tuned to reflect classes in supervised scenarios and clusters in unsupervised scenarios. The <i>n</i>-TARP method finds linear separations in high-dimensional data. This basic unit can be used repeatedly to find a variety of structures. It can be arranged in a hierarchical structure like a tree, which increases the model complexity, flexibility and discriminating power. Feature space extensions combined with <i>n</i>-TARP can also be used to investigate non-linear separations in high-dimensional data.<br></div><div><br></div><div>The application of <i>n</i>-TARP to both supervised and unsupervised problems is investigated in this dissertation. In the supervised scenario, a sequence of <i>n</i>-TARP based classifiers with increasing complexity is considered. The point separations are measured by classification metrics like accuracy, Gini impurity or entropy. The performance of these classifiers on image classification tasks is studied. This study provides an interesting insight into the working of classification methods. The sequence of <i>n</i>-TARP classifiers yields benchmark curves that put in context the accuracy and complexity of other classification methods for a given dataset. The benchmark curves are parameterized by classification error and computational cost to define a benchmarking plane. This framework splits this plane into regions of "positive-gain" and "negative-gain" which provide context for the performance and effectiveness of other classification methods. The asymptotes of benchmark curves are shown to be optimal (i.e. at Bayes Error) in some cases (Theorem 2.5.2).<br></div><div><br></div><div>In the unsupervised scenario, the <i>n</i>-TARP method highlights the existence of many different clustering structures in a dataset. However, not all structures present are statistically meaningful. This issue is amplified when the dataset is small, as random events may yield sample sets that exhibit separations that are not present in the distribution of the data. Thus, statistical validation is an important step in data analysis, especially in high-dimensions. However, in order to statistically validate results, often an exponentially increasing number of data samples are required as the dimensions increase. The proposed <i>n</i>-TARP method circumvents this challenge by evaluating statistical significance in the one-dimensional space of data projections. The <i>n</i>-TARP framework also results in several different statistically valid instances of point separation into clusters, as opposed to a unique "best" separation, which leads to a distribution of clusters induced by the random projection process.<br></div><div><br></div><div>The distributions of clusters resulting from <i>n</i>-TARP are studied. This dissertation focuses on small sample high-dimensional problems. A large number of distinct clusters are found, which are statistically validated. The distribution of clusters is studied as the dimensionality of the problem evolves through the extension of the feature space using monomial terms of increasing degree in the original features, which corresponds to investigating non-linear point separations in the projection space.<br></div><div><br></div><div>A statistical framework is introduced to detect patterns of dependence between the clusters formed with the features (predictors) and a chosen outcome (response) in the data that is not used by the clustering method. This framework is designed to detect the existence of a relationship between the predictors and response. This framework can also serve as an alternative cluster validation tool.<br></div><div><br></div><div>The concepts and methods developed in this dissertation are applied to a real world data analysis problem in Engineering Education. Specifically, engineering students' Habits of Mind are analyzed. The data at hand is qualitative, in the form of text, equations and figures. To use the <i>n</i>-TARP based analysis method, the source data must be transformed into quantitative data (vectors). This is done by modeling it as a random process based on the theoretical framework defined by a rubric. Since the number of students is small, this problem falls into the small sample high-dimensions scenario. The <i>n</i>-TARP clustering method is used to find groups within this data in a statistically valid manner. The resulting clusters are analyzed in the context of education to determine what is represented by the identified clusters. The dependence of student performance indicators like the course grade on the clusters formed with <i>n</i>-TARP are studied in the pattern dependence framework, and the observed effect is statistically validated. The data obtained suggests the presence of a large variety of different patterns of Habits of Mind among students, many of which are associated with significant grade differences. In particular, the course grade is found to be dependent on at least two Habits of Mind: "computation and estimation" and "values and attitudes."<br></div>

Newsvendor Models with Monte Carlo Sampling by Ijeoma Winifred Ekwegh The newsvendor model is used in solving inventory problems in which demand is random. In this thesis, we will focus on a method of using Monte Carlo sampling to estimate the order quantity that will either maximizes revenue or minimizes cost given that demand is uncertain. Given data, the Monte Carlo approach will be used in sampling data over scenarios and also estimating the probability density function. A bootstrapping process yields an empirical distribution for the order quantity that will maximize the expected profit. Finally, this method will be used on a newsvendor example to show that it works in maximizing profit.