<p dir="ltr">This dissertation addresses three progressively fundamental problems for functional data analysis: (1) To do efficient inference for the functional mean model accounting for within-subject correlation, we propose the refined and bias-corrected empirical likelihood method. (2) To identify functional subjects potentially from different populations, we propose the dominant-set based unsupervised clustering method using the similarity matrix. (3) To learn the similarity matrix from various similarity metrics for functional data clustering, we propose the modularity guided and dominant-set based semi-supervised clustering method.</p><p dir="ltr">In the first problem, the empirical likelihood method is utilized to do inference for the mean function of functional data by constructing the refined and bias-corrected estimating equation. The proposed estimating equation not only improves efficiency but also enables practically feasible empirical likelihood inference by properly incorporating within-subject correlation, which has not been achieved by previous studies.</p><p dir="ltr">In the second problem, the dominant-set based unsupervised clustering method is proposed to maximize the within-cluster similarity and applied to functional data with a flexible choice of similarity measures between curves. The proposed unsupervised clustering method is a hierarchical bipartition procedure under the penalized optimization framework with the tuning parameter selected by maximizing the clustering criterion called modularity of the resulting two clusters, which is inspired by the concept of dominant set in graph theory and solved by replicator dynamics in game theory. The advantage offered by this approach is not only robust to imbalanced sizes of groups but also to outliers, which overcomes the limitation of many existing clustering methods.</p><p dir="ltr">In the third problem, the metric-based semi-supervised clustering method is proposed with similarity metric learned by modularity maximization and followed by the above proposed dominant-set based clustering procedure. Under semi-supervised setting where some clustering memberships are known, the goal is to determine the best linear combination of candidate similarity metrics as the final metric to enhance the clustering performance. Besides the global metric-based algorithm, another algorithm is also proposed to learn individual metrics for each cluster, which permits overlapping membership for the clustering. This is innovatively different from many existing methods. This method is superiorly applicable to functional data with various similarity metrics between functional curves, while also exhibiting robustness to imbalanced sizes of groups, which are intrinsic to the dominant-set based clustering approach.</p><p dir="ltr">In all three problems, the advantages of the proposed methods are demonstrated through extensive empirical investigations using simulations as well as real data applications.</p>

<div>The orbits of interest for potential missions are stable or nearly stable to maintain long term presence for conducting scientific studies and to reduce the possibility of rapid departure. Near Rectilinear Halo Orbits (NRHOs) offer such stable or nearly stable orbits that are defined as part of the L1 and L2 halo orbit families in the circular restricted three-body problem. Within the Earth-Moon regime, the L1 and L2 NRHOs are proposed as long horizon trajectories for cislunar exploration missions, including NASA's upcoming Gateway mission. These stable or nearly stable orbits do not possess well-distinguished unstable and stable manifold structures. As a consequence, existing tools for stationkeeping and transfer trajectory design that exploit such underlying manifold structures are not reliable for orbits that are linearly stable. The current investigation focuses on leveraging stretching direction as an alternative for visualizing the flow of perturbations in the neighborhood of a reference trajectory. The information supplemented by the stretching directions are utilized to investigate the impact of maneuvers for two contrasting applications; the stationkeeping problem, where the goal is to maintain a spacecraft near a reference trajectory for a long period of time, and the transfer trajectory design application, where rapid departure and/or insertion is of concern.</div><div><br></div><div>Particularly, for the stationkeeping problem, a spacecraft incurs continuous deviations due to unmodeled forces and orbit determination errors in the complex multi-body dynamical regime. The flow dynamics in the region, using stretching directions, are utilized to identify appropriate maneuver and target locations to support a long lasting presence for the spacecraft near the desired path. The investigation reflects the impact of various factors on maneuver cost and boundedness. For orbits that are particularly sensitive to epoch time and possess distinct characteristics in the higher-fidelity ephemeris model compared to their CR3BP counterpart, an additional feedback control is applied for appropriate phasing. The effect of constraining maneuvers in a particular direction is also investigated for the 9:2 synodic resonant southern L2 NRHO, the current baseline for the Gateway mission. The stationkeeping strategy is applied to a range of L1 and L2 NRHOs, and validated in the higher-fidelity ephemeris model.</div><div><br></div><div>For missions with potential human presence, a rapid transfer between orbits of interest is a priority. The magnitude of the state variations along the maximum stretching direction is expected to grow rapidly and, therefore, offers information to depart from the orbit. Similarly, the maximum stretching in reverse time, enables arrival with a minimal maneuver magnitude. The impact of maneuvers in such sensitive directions is investigated. Further, enabling transfer design options to connect between two stable orbits. The transfer design strategy developed in this investigation is not restricted to a particular orbit but applicable to a broad range of stable and nearly stable orbits in the cislunar space, including the Distant Retrograde Orbit (DROs) and the Low Lunar Orbits (LLO) that are considered for potential missions. Examples for transfers linking a southern and a northern NRHO, a southern NRHO to a planar DRO, and a southern NRHO to a planar LLO are demonstrated.</div>

Topographic depressions are naturally occurring low land areas surrounded by areas of high elevations, also known as “pits” or “sinks”, on terrain surfaces. Traditional watershed modeling often neglects the potential effects of depressions by implementing removal (mostly filling) procedures on the digital elevation model (DEM) prior to the simulation of physical processes. The assumption is that all the depressions are either spurious in the DEM or of negligible importance for modeling results. However, studies suggested that naturally occurring depressions can change runoff response and connectivity in a watershed based on storage conditions and their spatial arrangement, e.g., shift active contributing areas and soil moisture distributions, and timing and magnitude of flow discharge at the watershed outlet. In addition, recent advances in remote sensing techniques, such as LiDAR, allow us to examine this modeling assumption because naturally occurring depressions can be represented using high-resolution DEM. This dissertation provides insights on the effects of depressions on overland flow processes at multiple spatial scales, from internal depression areas to the watershed scale, based on hydrologic connectivity metrics. Connectivity describes flow pathway connectedness and is assessed using geostatistical measures of heterogeneity in overland flow patterns, i.e., connectivity function and integral connectivity scale lengths. A new algorithm is introduced here to upscale connectivity metrics to large gridded patterns (i.e., with > 1,000,000 cells) using GPU-accelerated computing. This new algorithm is sensitive to changes of connectivity directions and magnitudes in spatial patterns and is robust for large DEM grids with depressions. Implementation of the connectivity metrics to overland flow patterns generated from original and depression filled DEMs for a study watershed indicates that depressions typically decrease overland flow connectivity. A series of macro connectivity stages based on spatial distances are identified, which represent changes in the interaction mechanisms between overland flow and depressions, i.e., the relative dominance of fill and spill, and the relative speed of fill and formation of connected pathways. In addition, to study the role of spatial resolutions on such interaction mechanisms at watershed scale, two revised functional connectivity metrics are also introduced, based on depressions that are hydraulically connected to the watershed outlet and runoff response to rainfall. These two functional connectivity metrics are sensitive to connectivity changes in overland flow patterns because of depression removal (filling) for DEMs at different grid resolutions. Results show that these two metrics indicate the spatial and statistical characteristics of depressions and their implications on overland flow connectivity, and may also relate to storage and infiltration conditions. In addition, grid resolutions have a more significant impact on overland flow connectivity than depression removal (filling).

Cluster robust models are a kind of statistical models that attempt to estimate parameters considering potential heterogeneity in treatment effects. Absent heterogeneity in treatment effects, the partial and average treatment effect are the same. When heterogeneity in treatment effects occurs, the average treatment effect is a function of the various partial treatment effects and the composition of the population of interest. The first chapter explores the performance of common estimators as a function of the presence of heterogeneity in treatment effects and other characteristics that may influence their performance for estimating average treatment effects. The second chapter examines various approaches to evaluating and improving cluster structures as a way to obtain cluster-robust models. Both chapters are intended to be useful to practitioners as a how-to guide to examine and think about their applications and relevant factors. Empirical examples are provided to illustrate theoretical results, showcase potential tools, and communicate a suggested thought process. The third chapter relates to an open-source statistical software package for the Julia language. The content includes a description for the software functionality and technical elements. In addition, it features a critique and suggestions for statistical software development and the Julia ecosystem. These comments come from my experience throughout the development process of the package and related activities as an open-source and professional software developer. One goal of the paper is to make econometrics more accessible not only through accessibility to functionality, but understanding of the code, mathematics, and transparency in implementations.

With the shift to learn and consume information through our mobile devices, most academic research is still only presented in long-form text. The Stanford Scholar Initiative has explored the segment of content creation and consumption of academic research through video. However, there has been another popular shift in presenting information from various social media platforms and media outlets in the past few years. Snapchat and Instagram have introduced the concept of tappable “Stories” that have gained popularity in the realm of content consumption. To accelerate the growth of the creation of these research talks, I propose an alternative to video: a tappable Snapchat-like interface. This style is achieved using AMP, Google’s open source project to optimize web experiences on mobile, and particularly the AMP Stories visual medium. My research seeks to explore how the process and quality of consuming the content of academic papers would change if instead of watching videos, users would consume content through Stories on mobile instead. Since this form of content consumption is still largely unresearched in the academic context, I approached this research with a human-centered design process, going through a few iterations to test various prototypes before formulating research questions and designing an experiment. I tested various formats of research consumption through Stories with pilot users, and learned many lessons to iterate from along the way. I created a way to consume research papers in a Stories format, and designed a comparative study to measure the effectiveness of consuming research papers through the Stories medium and the video medium. The results indicate that Stories are a quicker way to consume the same content, and improve the user’s pace of comprehension. Further, the Stories medium provides the user a self-paced method—both temporally and content-wise—to consume technical research topics, and is deemed as a less boring method to do so in comparison to video. While Stories gave the learner a chance to actively participate in consumption by tapping, the video experience is enjoyed because of its reduced effort and addition of an audio component. These findings suggest that the Stories medium may be a promising interface in educational contexts, for distributing scientific content and assisting with active learning.

The Brisbane Longitudinal Twin Study (BLTS) was being conducted in Australia and was funded by the US National Institute on Drug Abuse (NIDA). Adolescent twins were sampled as a part of this study and surveyed about their substance use as part of the Pathways to Cannabis Use, Abuse and Dependence project. The methods developed in this dissertation were designed for the purpose of analyzing a subset of the Pathways data that includes demographics, cannabis use metrics, personality measures, and imputed genotypes (SNPs) for 493 complete twin pairs (986 subjects.) The primary goal was to determine what combination of SNPs and additional covariates may predict cannabis use, measured on an ordinal scale as: “never tried,” “used moderately,” or “used frequently”. To conduct this analysis, we extended the ordinal Generalized Monotone Incremental Forward Stagewise (GMIFS) method for mixed models. This extension includes allowance for a unpenalized set of covariates to be coerced into the model as well as flexibility for user-specified correlation patterns between twins in a family. The proposed methods are applicable to high-dimensional (genomic or otherwise) data with ordinal response and specific, known covariance structure within clusters.

Widely effective treatment for alcohol use disorder is not yet available, because the exact biological mechanisms that underlie this disorder are not completely understood. One way to gain a better understanding of these mechanisms is to examine the genetic frameworks that contribute to the risk for developing this disorder. This dissertation examines genetic association data in combination with gene expression networks in the brain to identify functional groups of genes associated with alcohol consumption and dependence. The first study took advantage of the behavioral complexity of human samples, and experimental capabilities provided by mouse models, by co-analyzing gene expression networks in the mesolimbocortical system of acute alcohol-treated mice and human genetic alcohol dependence association data. This study successfully identified ethanol-responsive gene expression networks with overrepresentation of genes suggestively associated with alcohol dependence in an independent human sample, indicating that gene expression networks in mouse models are informative for identifying mechanistic networks relevant to the risk for developing dependence. The second study aimed to identify quantitative trait loci for voluntary alcohol drinking behaviors under an intermittent ethanol access paradigm, in the genetically complex Diversity Outbred mice. After determining high heritability for alcohol consumption and dependence amongst the progenitor strains, we identified several specific genetic loci associated with these traits. One locus replicated results from a human association study of alcohol consumption, and provided insight to the potentially contributing genes. Finally, we identified alcohol consumption-correlated gene expression networks in the prefrontal cortex of these mice. We also mapped quantitative trait loci for network expression levels, some of which overlapped with the behavioral loci, indicating that the functions represented by these modules mediate the relationship between the genotypes in that region and drinking behaviors. Overall, our studies revealed neuroplastic and ubiquitin-related genes pathways involved in alcohol consumption in mice and humans, and that likely contribute to the risk for developing dependence.

Multiple regression models play an important role in analyzing and making predictions about data. Prediction accuracy becomes lower when two or more explanatory variables in the model are highly correlated. One solution is to use ridge regression. The purpose of this thesis is to study the performance of available ridge regression estimators for Poisson regression models in the presence of moderately to highly correlated variables. As performance criteria, we use mean square error (MSE), mean absolute percentage error (MAPE), and percentage of times the maximum likelihood (ML) estimator produces a higher MSE than the ridge regression estimator. A Monte Carlo simulation study was conducted to compare performance of the estimators under three experimental conditions: correlation, sample size, and intercept. It is evident from simulation results that all ridge estimators performed better than the ML estimator. We proposed new estimators based on the results, which performed very well compared to the original estimators. Finally, the estimators are illustrated using data on recreational habits.

Fatal automobile crashes have claimed the lives of over 33,000 people each year in the United States since 1995. As in any point event, fatal crash events do not occur randomly in time or space. The objectives of this study were to identify spatial patterns and hot spots in FARS (Fatal Analysis Reporting System) fatal crash events based on temporal and demographic characteristics. The methods employed included 1) rate calculation using FARS points and average daily traffic flow; 2) planar kernel density estimation of FARS crash events based on temporal and demographic attributes within the data; and 3) two case studies using network kernel density estimation along roadways to determine hot spots fatal crashes in Jefferson County and Warren County. Rate calculation analyses revealed that travel on roads with high speed limits and winding topography led to the highest number of crashes and highest rate of fatal crashesper 1,000 daily vehicles. Planar kernel density estimation results showed temporalpatterns, revealing that ‘hot spots’ and fatalities were highest in the summer, and typically occurred from 2pm-6pm on the weekends. Further, the 16 to 25 year age group was responsible for the most significant ‘hot spots’ and the most fatal accidents. Also showing that the most significant hot spots involving alcohol occurring in close proximity to meeting places such as bars and restaurants. Finally, results from the network kernel density estimation revealed that most hot spots were in high traffic areas of where majorr oads converged with secondary roads.

The combination of analytical sensitivity and selectivity provided by time-of-flight secondary ion mass spectrometry (ToF-SIMS), with advanced statistical interrogation by principal component analysis (PCA), has allowed a significant advancement in the forensic discrimination of pen, pencil and glass materials based on trace characterisation.