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This dissertation is comprised of three parts. The first proposes a sequential approach to determine the experimental setting with the minimum variance (Kerfonta et al., 2024). Two acquisition functions are developed to assist developing the approach. Theoretical results along with a case study using data from crystallization experiments is conducted to show the ability of the proposed method to correctly select the experiment with the minimum variance. The second and third parts propose adaptations to the Bayesian optimization algorithm using transformed additive Gaussian processes (TAG) as the surrogate model. The goal of using the TAG framework is to decompose the optimization problem into multiple one-dimensional optimization problems. The second part of this dissertation proposes a Bayesian optimization algorithm for single objective optimization using TAG as the surrogate model and a modified expected improvement acquisition function. To demonstrate the advantages of the proposed method, it will be compared to Bayesian optimization with a Gaussian process surrogate model using the expected improvement acquisition function. The final part of this dissertation proposes a bi-objective Bayesian optimization algorithm that uses TAG as the surrogate model and a modified expected hypervolume improvement acquisition function. This approach is compared to classical bi-objective Bayesian optimization using a Gaussian process surrogate model. Functions from existing bi-objective optimization literature are used to demonstrate the advantages of the proposed method.

Biomedical text is being generated at a high rate in scientific literature publications and electronic health records. Within these documents lies a wealth of potentially useful information in biomedicine. Relation extraction (RE), the process of automating the identification of structured relationships between entities within text, represents a highly sought-after goal in biomedical informatics, offering the potential to unlock deeper insights and connections from this vast corpus of data. In this dissertation, we tackle this problem with a variety of approaches. We review the recent history of the field of document-level RE. Several themes emerge. First, graph neural networks dominate the methods for constructing entity and relation representations. Second, clever uses of attention allow for the these constructions to focus on particularly relevant tokens and object (such as mentions and entities) representations. Third, aggregation of signal across mentions in entity-level RE is a key focus of research. Fourth, the injection of additional signal by adding tokens to the text prior to encoding via language model (LM) or through additional learning tasks boosts performance. Last, we explore an assortment of strategies for the challenging task of end-to-end entity-level RE. Of particular note are sequence-to-sequence (seq2seq) methods that have become particularly popular in the past few years. With the success of general-domain generative LMs, biomedical NLP researchers have trained a variety of these models on biomedical text under the assumption that they would be superior for biomedical tasks. As training such models is computationally expensive, we investigate whether they outperform generic models. We test this assumption rigorously by comparing performance of all major biomedical generative language models to the performances of their generic counterparts across multiple biomedical RE datasets, in the traditional finetuning setting as well as in the few-shot setting. Surprisingly, we found that biomedical models tended to underperform compared to their generic counterparts. However, we found that small-scale biomedical instruction finetuning improved performance to a similar degree as larger-scale generic instruction finetuning. Zero-shot natural language processing (NLP) offers savings on the expenses associated with annotating datasets and the specialized knowledge required for applying NLP methods. Large, generative LMs trained to align with human objectives have demonstrated impressive zero-shot capabilities over a broad range of tasks. However, the effectiveness of these models in biomedical RE remains uncertain. To bridge this gap in understanding, we investigate how GPT-4 performs across several RE datasets. We experiment with the recent JSON generation features to generate structured output, which we use alternately by defining an explicit schema describing the relation structure, and inferring the structure from the prompt itself. Our work is the first to study zero-shot biomedical RE across a variety of datasets. Overall, performance was lower than that of fully-finetuned methods. Recall suffered in examples with more than a few relations. Entity mention boundaries were a major source of error, which future work could fruitfully address. In our previous work with generative LMs, we noted that RE performance decreased with the number of gold relations in an example. This observation aligns with the general pattern that recurrent neural network and transformer-based model performance tends to decrease with sequence length. Generative LMs also do not identify textual mentions or group them into entities, which are valuable information extraction tasks unto themselves. Therefore, in this age of generative methods, we revisit non-seq2seq methodology for biomedical RE. We adopt a sequential framework of named entity recognition (NER), clustering mentions into entities, followed by relation classification (RC). As errors early in the pipeline necessarily cause downstream errors, and NER performance is near its ceiling, we focus on improving clustering. We match state-of-the-art (SOTA) performance in NER, and substantially improve mention clustering performance by incorporating dependency parsing and gating string dissimilarity embeddings. Overall, we advance the field of biomedical RE in a few ways. In our experiments of finetuned LMs, we show that biomedicine-specific models are unnecessary, freeing researchers to make use of SOTA generic LMs. The relatively high few-shot performance in these experiments also suggests that biomedical RE can be reasonably accessible, as it is not so difficult to construct small datasets. Our investigation into zero-shot RE shows that SOTA LMs can compete with fully finetuned smaller LMs. Together these studies also demonstrate weaknesses of generative RE. Last, we show that non-generative RE methods still outperform generative methods in the fully-finetuned setting.

The ocean remains severely under-observed, in part due to its sheer size. Containing nearly billion of water with most of the subsurface being invisible because water is extremely difficult to penetrate using electromagnetic radiation, as is typically used by satellite measuring instruments. For this reason, most observations of the ocean have very low spatial-temporal coverage to get a broad capture of the ocean’s features. However, recent “dense but patchy” data have increased the availability of high-resolution – low spatial coverage observations. These novel data sets have motivated research into multi-scale data assimilation methods. Here, we demonstrate a new assimilation approach utilizing the wavelet transform that is multi-scale by nature but only requires a single analysis step; the latter being a significant advancement over current multi-scale approaches that almost universally require at least two analysis steps. To produce a proof-of-concept, we utilize only sea surface temperature (SST), as that observational source has strong spatial coverage and is high-resolution. The current standard when assimilating SST is to first perform super observations. The super-observation approach reduces a dense field to weighted averaged points that are far enough away from each other such that their readings are statistically uncorrelated. The process typically reduces an SST field to less than 10% of the original size, leading to only large-scale corrections of the ocean model. Our advancement instead uses the wavelet transform as an “observational operator”. The wavelet transform allows the SST innovation to occur in wavelet space, and wavelet thresholding allows us to retain all the spatial information in the SST field, down to scales that are not well represented by the horizontal resolution of the ocean model. An Observing System Simulation Experiment (OSSE) was used to test the validity of using wavelets in data assimilation. We find that the wavelet-based assimilation produces less root mean square (RMS) error with respect to depth than the more traditional super-observation approach. Additionally, we evaluated the spatial scales constrained by each assimilation approach. We find that over a 31-day cycling experiment, the wavelet-based approach constrains 65.50 versus the super-observation, a 14% gain in assimilation skill for the wavelet method. By constraining roughly 10 km more wavelength in the assimilation, the wavelet-based approach will now allow the representation of ocean features in the 76-65km range, which were previously not present from using super-observations. We expect this is due explicitly to the fact that the wavelet transform allows the assimilation to consider many more spatial scales than is possible using the super-observation approach.

The developed methodologies are proposed to serve as support for control centers and fault analysis engineers. These approaches provide a dependable and effective means of pinpointing and resolving faults, which ultimately enhances power grid reliability. The algorithm uses the Least Absolute Value (LAV) method to estimate the augmented states of the PCB, enabling supervisory monitoring of the system. In addition, the application of statistical analysis based on projection statistics of the system Jacobian as a virtual sensor to detect faults on transmission lines. This approach is particularly valuable for detecting anomalies in transmission line data, such as bad data or other outliers, and leverage points. Through the integration of remote PCB status with virtual sensors, it becomes possible to accurately detect faulted transmission lines within the system. This, in turn, saves valuable troubleshooting time for line engineers, resulting in improved overall efficiency and potentially significant cost savings for the company. When there is a temporary or permanent fault, the generator dynamics will be affected by the transmission line reclosing, which could impact the system's stability and reliability. To address this issue, an unscented Kalman filter (UKF) and optimal performance iterated unscented Kalman filter (IUKF) dynamic state estimation techniques are proposed. These techniques provide an estimate of the dynamic states of synchronous generators, which is crucial for monitoring generator states during transmission lines reclosing for temporary and permanent fault conditions. Several test systems were employed to evaluate reclosing following faults on transmission lines, including the IEEE 14-bus system, Kundur's two-area model, and the reduced Western Electricity Coordinating Council (WECC) model of UTK electrical engineering hardware test bed (HTB). The developed methods offer a comprehensive solution to address the challenges posed by unbalanced faults on transmission lines, such as line-to-line, line-to-line-ground, and line-to-ground faults. Utilities must consider these faults when developing protective settings. The effectiveness of the solution is confirmed by monitoring the reaction of dynamic state variables following transmission lines reclosing after temporary faults and transmission line lockout from permanent faults.

This dissertation aims to extend the boundaries of Programming Computable Functions (PCF) by introducing a novel collection of categories referred to as Random Variable Spaces. Originating as a generalization of Quasi-Borel Spaces, Random Variable Spaces are rigorously defined as categories where objects are sets paired with a collection of random variables from an underlying measurable space. These spaces offer a theoretical foundation for extending PCF to natively handle stochastic elements. The dissertation is structured into seven chapters that provide a multi-disciplinary background, from PCF and Measure Theory to Category Theory with special attention to Monads and the Giry Monad. The crux of the dissertation lies in the detailed exploration of Random Variable Spaces. Their mathematical properties are studied, including the establishment of relationships between these spaces through functors based on measurable functions. Additionally, the dissertation investigates the possibility of a fibration between the category of Measurable Spaces (Meas) and Random Variable Spaces. While such a fibration is not found, it offers an alternative fibration after particular alterations are made to Meas. Further, the work culminates in an extension to PCF, introducing computational rules to accommodate random variables. The dissertation provides a formal proof of correctness for these new rules, validating the extended framework's reliability. The dissertation makes contributions to the fields of mathematical logic and computation. It not only extends PCF in a significant manner but also lays the groundwork for future research in Random Variable Spaces and their applicability to the theory of computation. With its focus on allowing PCF to natively handle stochastic elements, this dissertation aims to enrich our understanding of computation in an increasingly complex and probabilistic world.

This thesis focuses on methods for improving energy consumption prediction performance in complex industrial machines. Working with real-world industrial machines brings several challenges, including data access, algorithmic bias, data privacy, and the interpretation of machine learning algorithms. To effectively manage energy consumption in the industrial sector, it is essential to develop a framework that enhances prediction performance, reduces energy costs, and mitigates air pollution in heavy industrial machine operations. This study aims to assist managers in making informed decisions and driving the transition towards green manufacturing. The energy consumption of industrial machinery is substantial, and the recent increase in CO2 emissions is a major concern. Consequently, energy efficiency is becoming gradually more crucial for businesses, governments, and the environment. Accurately estimating the power consumption of industrial machines might be useful in adjusting machine operation settings for operators. Smart devices can help manage electricity consumption more efficiently by providing necessary data that can be used to make better decisions. However, datasets from real-world industrial machines often contain several challenges, including unexpected changes over time, inconsistent operating conditions, missing data, unknown working environments, unrecorded maintenance, and human errors. The utilization of energy consumption patterns can enable more accurate calculation methods. Precisely predicting the energy consumption of heavy industrial machines is fundamental for enhancing energy efficiency and minimizing blackouts. While numerous research papers have concentrated on improving the prediction accuracy of traditional static machine learning models, these models may not perform well as data evolves by time. The presence of expected or unexpected variations, known as concept drift, can have a significant impact on the performance of machine learning models over time. Therefore, it is crucial to design a method that takes these potential changes into account when predicting power consumption for industrial machines. A novel data-driven dynamic modeling approach was developed in this dissertation to detect repetitive machine running regimes and improve the prediction accuracy of energy usage for industrial machines. All designed methods, including traditional static modeling, were applied to three distinct real-world industrial machine datasets. The experimental results obtained from these implementations are thoroughly discussed and presented in detail. In the first part of the dissertation, the proposed multi-regime approach successfully detects repeated machine multi-regime running conditions and maintains a better overall prediction performance over time compared to other methods. Secondly, the designed dynamic method for predicting energy consumption of industrial machines under repetitive regimes outperforms traditional static modeling and ensemble modeling in real-time prediction. Lastly, the implemented statistical tests demonstrated that the proposed dynamic method achieved a significant improvement in prediction performance accuracy compared to the other applied methods. According to the experimental results, the developed dynamic modeling proves to be applicable to various industrial machines with complex structures and features, delivering a more precise prediction performance. As a result of this study, companies can gain a better understanding of their machine working conditions and make necessary adaptations to decrease their energy consumption over time. Overall, this dissertation emphasizes the importance of industrial machine data in the energy sector and the potential for data-driven solutions to enhance energy efficiency in industrial machinery. The ultimate goal is to encourage further research in energy efficiency with the aim of reducing air pollution and facilitating a timely transition towards green manufacturing.

Networks have the critical ability to represent the complex interconnectedness of social relationships, biological processes, and the spread of diseases and information. Exponential random graph models (ERGM) are one of the popular statistical methods for analyzing network data. ERGM, however, struggle with computational challenges and degeneracy issues, further exacerbated by their inability to handle high-dimensional network data. Bayesian techniques provide a promising avenue to overcome these two problems. This paper considers penalized Bayesian exponential random graph models with adaptive lasso and adaptive ridge penalties to perform variable selection and reduce multicollinearity on a variety of networks. The experimental results demonstrate their effectiveness in variable selection and reduction of multicollinearity across diverse networks, outperforming the widely used Bayesian exponential random graph model proposed by Caimo et al., which lacks regularization capabilities. This paper presents a valuable extension to network models for large-scale high-dimensional data and offers opportunities for advancing research in diverse fields.

Mental health is quickly becoming a major policy concern, with recent data reporting increasing and disproportionately worse mental health outcomes, including anxiety, depression, increased substance abuse, and elevated suicidal ideation. One specific population that is especially high risk for these issues is the military community because military conflict, deployment stressors, and combat exposure contribute to the risk of mental health problems. Although several pharmacological approaches have been employed to combat this epidemic, their efficacy is mixed at best, which has led to novel nonpharmacological approaches. One such approach is Operation Surf, a nonprofit that provides nature-based programs advocating the restorative power of the ocean and surfing. Although the limited research in this area has shown a positive impact on the health of veterans, these results were based on self-reported survey instruments that suffer from a series of well-known biases. Fortunately, the recent introduction of wearable technology (e.g., Whoop bands) that unobtrusively gather physiological data such as heart rate variability (HRV), resting heart rate (RHR), and both rapid eye movement (REM) and deep sleep, offers an opportunity to validate or invalidate traditional survey assessment data. This study used survey data to measure changes in depression, anxiety, and posttraumatic stress disorder (PTSD), together with data generated from Whoop bands, and qualitative data, producing a more robust set of programmatic efficacy inferences for military veterans who participated in Operation Surf between 2021–2022. Paired samples t tests were used to analyze the data gathered before the intervention, immediately after, and 1 month later. Survey scores before the therapy, as measured by the psychometrically sound PHQ-8 (depression), PCL-5 (PTSD), and GAD-7 (anxiety), were significantly higher than both time points after therapy, revealing statistically significant and clinically significant decreases in anxiety, depression, and PTSD symptoms. Physiological data indicated varying degrees of statistically significant change in HRV, RHR, REM sleep, and deep sleep, while the qualitative data provided supported the quantitative findings. Taken together, the introduction of physiological data gathered from wearable technology can hopefully further understanding toward a low-cost, scalable treatment modality while eliminating stigmas and barriers to care for military veterans and informing public policy care decisions.

This thesis delves into cybersecurity by applying Deep Reinforcement(DRL) Learning in network intrusion detection. One advantage of DRL is the ability to adapt to changing network conditions and evolving attack methods, making it a promising solution for addressing the challenges involved in intrusion detection. The thesis will also discuss the obstacles and benefits of using Classification methods for network intrusion detection and the need for high-quality training data. To train and test our proposed method, the NSL-KDD dataset was used and then adjusted by converting it from a multi-classification to a binary classification, achieved by joining all attacks into one. This approach sets apart our research from other studies.

This dissertation studies a Lindley random walk model when the increment process driving the walk is strictly stationary. Lindley random walks govern customer waiting times in many queueing models and several natural and business processes, including snow depths, frozen soil depths, inventory quantities, etc. Probabilistic properties of a Lindley process with time-correlated stationary changes are explored. We provide a streamlined argument that the process admits a limiting stationary distribution when the mean of the incremental changes is negative and that the Lindley process is strictly stationary when starting from this stationary distribution. The Markov characteristics of the process are explored when the change process has a Markov structure of first or higher order. A derivation of the model's likelihood is given when the change process obeys a pth order autoregression. Due to the unwieldy nature of this likelihood, a particle filtering method of evaluating and optimizing it is devised and studied via simulation.

When building models to investigate outcomes and variables of interest, researchers often want to adjust for other variables. There is a variety of ways that these adjustments are performed. In this work, we will consider four approaches to adjustment utilized by researchers in various fields. We will compare the efficacy of these methods to what we call the ”true model method”, fitting a multiple linear regression model in which adjustment variables are model covariates. Our goal is to show that these adjustment methods have inferior performance to the true model method by comparing model parameter estimates, power, type I error, model fit statistics, and residuals. First, we evaluate the “subtraction adjustment method”. This is used for variables like pre and post blood glucose levels. In this method, one adjusts for the pre value by subtracting it from the post value, with this difference being the new outcome. Next, we evaluate the “division adjustment method”. This occurs when researchers adjust an outcome by dividing it by a variable such as body mass, with the result being the new outcome. The third method investigated is the “residual adjustment method”, where a model is fit first on the adjustment variable to obtain those residuals. Then, those residuals are fit on the variable of interest. This has been used in human GWAS studies, sometimes called “two-stage regression analysis.” The final method we investigated is Nanostring’s method for normalizing genetic data. This is a multistep process used in their software to adjust for variability in their ma-chines’ assay process. To test these methods, we performed simulations to evaluate how these methods perform with and without an interaction effect in the data. We found cases where the models created using these methods could not accurately estimate the model coefficients. In addition, they completely miss interaction effects, and contain the potential for masking significant associations between the outcome and variable of interest. Perhaps most troubling was how some of the methods were found to have lower power than simply fitting a linear regression model using adjustment variables as covariates. Finally, even when the models from the adjustment methods had comparable performance to the true model method, the model fit (measured by adjusted R2) was inferior to the true model method. Because of this, we advocate that variable adjustments be done via adding them as covariates, rather than using these methods to create adjusted outcomes.

The demand for statistical knowledge and skills is growing in many disciplines, so more students are enrolling in introductory statistics courses (Blair, Kirkman, & Maxwell, 2018). At the same time, institutions are seeking course delivery methods that allow for greater flexibility for students, especially following the onset of the COVID-19 pandemic; therefore, there is more interest in the development and delivery of online introductory statistics courses. To address this, I collaboratively designed an online introductory statistics course which focuses on simulation-based inference for the University of Nebraska-Lincoln. The course design was informed by the Community of Inquiry framework (Garrison, Anderson, & Archer, 2000). The course is delivered asynchronously and has the capacity for high enrollment. Following the development of the course, I co-taught this course from Fall 2018 to Spring 2021 and recruited enrolled students to participate in my study. Participants granted research access to several components of their normal coursework and completed three surveys: Survey of Attitudes Toward Statistics (36-question version pre-test and post-test; Schau, 2003a, 2003b) and the Distance Education and Technological Advancements Survey (Joosten & Reddy, 2015). The primary goal of this study was to understand factors that influence student outcomes in this course. An intervention was designed to support the community of inquiry within the course and was implemented during Fall 2019 and Fall 2020. Using Bayesian hierarchical models, there was no evidence of an effect of the intervention on student outcomes. However, there were a variety of other self-reported factors that were found to be associated with student outcomes. The secondary aim of the study was to understand whether students' attitudes toward statistics changed during the term; however, descriptive statistics suggest that students' attitudes did not change during the term. To address some of the limitations of this study, future research could examine these research questions for simulation-based introductory statistics courses across multiple institutions. This study may help create recommendations for developing online introductory statistics courses. Adviser: Erin E. Blankenship