The shrinkage estimation has proven to be very useful when dealing with a large number of mean parameters. In this dissertation, we consider the problem of simultaneous estimation of multiple variances and construct a shrinkage type, non-parametric estimator. We take the non-parametric empirical Bayes approach by starting with an arbitrary prior on the variances. Under an invariant loss function, the resultant Bayes estimator relies on the marginal cumulative distribution function of the sample variances. Replacing the marginal cdf by the empirical distribution function, we obtain a Non-parametric Empirical Bayes estimator for multiple Variances (NEBV). The proposed estimator converges to the corresponding Bayes version uniformly over a large set. Consequently, the NEBV works well in a post-selection setting. We then apply the NEBV to construct condence intervals for mean parameters in a post-selection setting. It is shown that the intervals based on the NEBV are shortest among all the intervals which guarantee a desired coverage probability. Through real data analysis, we have further shown that the NEBV based intervals lead to the smallest number of discordances, a desirable property when we are faced with the current "replication crisis". / Statistics

We present a system for the inference of various static properties from source code written in the Maple programming language. We make use of an abstract interpretation framework in the design of these properties and define languages of constraints specific to our abstract domains which capture the desired static properties of the code. Finally we discuss the automated generation and solution of these constraints, describe a tool for doing so, and present some results from applying this tool to several nontrivial test inputs. / Thesis / Master of Science (MSc)

There still is a practical need for improved closure models for the Reynolds-averaged Navier-Stokes (RANS) equations. This dissertation explores two different approaches for using experimental data to provide improved closure for the Reynolds stress tensor field. The first approach uses machine learning to learn a general closure model from data. A novel framework is developed to train deep neural networks using experimental velocity and pressure measurements. The sensitivity of the RANS equations to the Reynolds stress, required for gradient-based training, is obtained by means of both variational and ensemble methods. The second approach is to infer the Reynolds stress field for a flow of interest from limited velocity or pressure measurements of the same flow. Here, this field inversion is done using a Monte Carlo Bayesian procedure and the focus is on improving the inference by enforcing known physical constraints on the inferred Reynolds stress field. To this end, a method for enforcing boundary conditions on the inferred field is presented. The two data-driven approaches explored and improved upon here demonstrate the potential for improved practical RANS predictions. / Doctor of Philosophy / The Reynolds-averaged Navier-Stokes (RANS) equations are widely used to simulate fluid flows in engineering applications despite their known inaccuracy in many flows of practical interest. The uncertainty in the RANS equations is known to stem from the Reynolds stress tensor for which no universally applicable turbulence model exists. The computational cost of more accurate methods for fluid flow simulation, however, means RANS simulations will likely continue to be a major tool in engineering applications and there is still a need for improved RANS turbulence modeling. This dissertation explores two different approaches to use available experimental data to improve RANS predictions by improving the uncertain Reynolds stress tensor field. The first approach is using machine learning to learn a data-driven turbulence model from a set of training data. This model can then be applied to predict new flows in place of traditional turbulence models. To this end, this dissertation presents a novel framework for training deep neural networks using experimental measurements of velocity and pressure. When using velocity and pressure data, gradient-based training of the neural network requires the sensitivity of the RANS equations to the learned Reynolds stress. Two different methods, the continuous adjoint and ensemble approximation, are used to obtain the required sensitivity. The second approach explored in this dissertation is field inversion, whereby available data for a flow of interest is used to infer a Reynolds stress field that leads to improved RANS solutions for that same flow. Here, the field inversion is done via the ensemble Kalman inversion (EKI), a Monte Carlo Bayesian procedure, and the focus is on improving the inference by enforcing known physical constraints on the inferred Reynolds stress field. To this end, a method for enforcing boundary conditions on the inferred field is presented. While further development is needed, the two data-driven approaches explored and improved upon here demonstrate the potential for improved practical RANS predictions.

Modern radar systems must operate in a wide variety of time-varying conditions. These include various types of interference from neighboring systems, self-interference or clutter, and targets with fluctuating responses. It has been well-established that the quality and nature of radar measurements depend heavily on the choice of signal transmitted by the radar. In this dissertation, we discuss techniques which may be used to adapt the radar's waveform on-the-fly while making very few a priori assumptions about the physical environment. By employing tools from reinforcement learning and online learning, we present a variety of algorithms which handle practical issues of the waveform selection problem that have been left open by previous works. In general, we focus on two key challenges inherent to the waveform selection problem, sample-efficiency and universality. Sample-efficiency corresponds to the number of experiences a learning algorithm requires to achieve desirable performance. Universality refers to the learning algorithm's ability to achieve desirable performance across a wide range of physical environments. Specifically, we develop a contextual bandit-based approach to vastly improve the sample-efficiency of learning compared to previous works. We then improve the generalization performance of this model by developing a Bayesian meta-learning technique. To handle the problem of universality, we develop a learning algorithm which is asymptotically optimal in any Markov environment having finite memory length. Finally, we compare the performance of learning-based waveform selection to fixed rule-based waveform selection strategies for the scenarios of dynamic spectrum access and multiple-target tracking. We draw conclusions as to when learning-based approaches are expected to significantly outperform rule-based strategies, as well as the converse. / Doctor of Philosophy / Modern radar systems must operate in a wide variety of time-varying conditions. These include various types of interference from neighboring systems, self-interference or clutter, and targets with fluctuating responses. It has been well-established that the quality and nature of radar measurements depend heavily on the choice of signal transmitted by the radar. In this dissertation, we discuss techniques which may be used to adapt the radar's waveform on-the-fly while making very few explicit assumptions about the physical environment. By employing tools from reinforcement learning and online learning, we present a variety of algorithms which handle practical and theoretical issues of the waveform selection problem that have been left open by previous works. We begin by asking the questions "What is cognitive radar?" and "When should cognitive radar be used?" in order to develop a broad mathematical framework for the signal selection problem. The latter chapters then deal with the role of intelligent real-time decision-making algorithms which select favorable signals for target tracking and interference mitigation. We conclude by discussing the possible roles of cognitive radar within future wireless networks and larger autonomous systems.

Increases in demand have driven the development of complex processing technology for separating mineral resources from exceedingly low grade multi- component resources. Low mineral concentrations and variable feedstocks can make separating signal from noise difficult, while high process complexity and the multi-component nature of a feedstock can make testwork, optimization, and process simulation difficult or infeasible. A prime example of such a scenario is the recovery and separation of rare earth elements (REEs) and other critical minerals from acid mine drainage (AMD) using a solvent extraction (SX) process. In this process the REE concentration found in an AMD source can vary site to site, and season to season. SX processes take a non-trivial amount of time to reach steady state. The separation of numerous individual elements from gangue metals is a high-dimensional problem, and SX simulators can have a prohibitive computation time. Bayesian statistical methods intrinsically quantify uncertainty of model parameters and predictions given a set of data and a prior distribution and model parameter prior distributions. The uncertainty quantification possible with Bayesian methods lend well to statistical simulation, model selection, and sensitivity analysis. Moreover, Bayesian models utilizing Gaussian Process priors can be used for active learning tasks which allow for prediction, optimization, and simulator calibration while reducing data requirements. However, literature on Bayesian methods applied to separations engineering is sparse. The goal of this dissertation is to investigate, illustrate, and test the use of a handful of Bayesian methods applied to process engineering problems. First further details for the background and motivation are provided in the introduction. The literature review provides further information regarding critical minerals, solvent extraction, Bayeisan inference, data reconciliation for separations, and Gaussian process modeling. The body of work contains four chapters containing a mixture of novel applications for Bayesian methods and a novel statistical method derived for the use with the motivating problem. Chapter topics include Bayesian data reconciliation for processes, Bayesian inference for a model intended to aid engineers in deciding if a process has reached steady state, Bayesian optimization of a process with unknown dynamics, and a novel active learning criteria for reducing the computation time required for the Bayesian calibration of simulations to real data. In closing, the utility of a handfull of Bayesian methods are displayed. However, the work presented is not intended to be complete and suggestions for further improvements to the application of Bayesian methods to separations are provided. / Doctor of Philosophy / Rare earth elements (REEs) are a set of elements used in the manufacture of supplies used in green technologies and defense. Demand for REEs has prompted the development of technology for recovering REEs from unconventional resources. One unconventional resource for REEs under investigation is acid mine drainage (AMD) produced from the exposure of certain geologic strata as part of coal mining. REE concentrations found in AMD are significant, although low compared to REE ore, and can vary from site to site and season to season. Solvent extraction (SX) processes are commonly utilized to concentrate and separate REEs from contaminants using the differing solubilities of specific elements in water and oil based liquid solutions. The complexity and variability in the processes used to concentrate REEs from AMD with SX motivates the use of modern statistical and machine learning based approaches for filtering noise, uncertainty quantification, and design of experiments for testwork, in order to find the truth and make accurate process performance comparisons. Bayesian statistical methods intrinsically quantify uncertainty. Bayesian methods can be used to quantify uncertainty for predictions as well as select which model better explains a data set. The uncertainty quantification available with Bayesian models can be used for decision making. As a particular example, the uncertainty quantification provided by Gaussian process regression lends well to finding what experiments to conduct, given an already obtained data set, to improve prediction accuracy or to find an optimum. However, literature is sparse for Bayesian statistical methods applied to separation processes. The goal of this dissertation is to investigate, illustrate, and test the use of a handful of Bayesian methods applied to process engineering problems. First further details for the background and motivation are provided in the introduction. The literature review provides further information regarding critical minerals, solvent extraction, Bayeisan inference, data reconciliation for separations, and Gaussian process modeling. The body of work contains four chapters containing a mixture of novel applications for Bayesian methods and a novel statistical method derived for the use with the motivating problem. Chapter topics include Bayesian data reconciliation for processes, Bayesian inference for a model intended to aid engineers in deciding if a process has reached steady state, Bayesian optimization of a process with unknown dynamics, and a novel active learning criteria for reducing the computation time required for the Bayesian calibration of simulations to real data. In closing, the utility of a handfull of Bayesian methods are displayed. However, the work presented is not intended to be complete and suggestions for further improvements to the application of Bayesian methods to separations are provided.

Inference generation is a process that is key to successful reading (e.g., Bowyer- Crane and Snowling, 2005; Oakhill and Cain, 2012) and that begins to develop early in the reading acquisition process, through listening comprehension (e.g., Kendeou et al., 2009). Despite being able to generate inferences, such as cause and effect, as early as four years old (Lynch and van den Broek, 2007) inference generation is a skill not explicitly taught to many emergent readers. This study looked at wordless picturebooks and how they could be used with linguistic prompting to develop inferential thinking in young readers, building on the work of Grolig et al. (2020). The study involved a a quasi-experimental, 2-between subjects (wordless/worded picturebooks) and 2-within subjects (pre/post-assessment) design examining the impact of a reading intervention on emergent readers' inferential narrative comprehension. One group's intervention utilized wordless picturebooks, while the second group used a worded picturebook. The gains from pre- to post-assessment suggested that wordless picturebooks, alongside the planned prompts, did have an impact on the inferential narrative comprehension of the students (t (35) = 4.99, d = 1.63, p<.001) and that the intervention as a whole positively impacts members of both groups. / Doctor of Philosophy / As teachers, we want the children in our care to become strong readers. A part of this challenging task involves helping our students understand what they read. Wordless picturebooks, in combination with prompts for reading them, may be just the tool to help build comprehension through building inference making skills. This study looked at the impact of a wordless picturebook intervention on the inference generation abilities of young readers and found that wordless picturebooks, along with intentionally planned prompts to support readers, positively impacts a child's ability to make inferences.

Gene regulatory networks (GRNs) provide a natural representation of relationships between regulators and target genes. Though inferring GRN is a challenging task, many methods, including unsupervised and supervised approaches, have been developed in the literature. However, most of these methods target non-context-specific GRNs. Because the regulatory relationships consistently reprogram under different tissues or biological processes, non-context-specific GRNs may not fit some specific conditions. In addition, a detailed investigation of the prediction results has remained elusive. In this study, I propose to use a machine learning approach to predict GRNs that occur in developmental stage-specific networks and to show how it improves our understanding of the GRN in seed development. I developed a Beacon GRN inference tool to predict a GRN in seed development in Arabidopsis based on a support vector machine (SVM) local model. Using the time series gene expression levels in seed development and prior known regulatory relationships, I evaluated and predicted the GRN at this specific biological process. The prediction results show that one gene may be controlled by multiple regulators. The targets that are strongly positively correlated with their regulators are mostly expressed at the beginning of seed development. The direct targets were detected when I found a match between the promoter regions of the targets and the regulator's binding sequence. Our prediction provides a novel testable hypotheses of a GRN in seed development in Arabidopsis, and the Beacon GRN inference tool provides a valuable model system for context-specific GRN inference. / Master of Science

Enabling machines to interact with humans requires understanding what people mean, even when they do not say it explicitly. For example, machines should understand that ``selfish people oppose gun control'' implies a pro-gun control viewpoint (i.e., is taking a stance in support of gun control) despite the negative tone of the statement. Understanding these types of pragmatic inferences allows humans to grasp meaning (e.g., intentions, relevant facts) beyond what is literally expressed in an utterance. Furthermore, pragmatic inferences conveyed through generalizations (e.g., referring to generic ``selfish people'' rather than specific individuals in order to be more persuasive) support flexible and efficient reasoning. Therefore, in this thesis we focus on improving computational understanding of two inter-related types of pragmatic inferences: stancetaking and linguistic generalizations. This thesis is divided into two parts. In Part II, we focus on stance detection. One major challenge for stance detection models is the large and continually growing set of stance targets (i.e., topics to take a stance on). Therefore, to address this we define and study zero-shot stance detection (i.e., evaluation on topics for which there is no training data). Our work develops both datasets and models for this task and analyzes the ongoing challenges for future work. This work has stimulated increasing and ongoing research in zero-shot stance detection in NLP. Then in Part I we study generics --- a specific type of linguistic generalization that does not contain explicit quantifiers (e.g., ``most'', ``some''). These statements can have strong persuasive force and are also related to complex patterns of reasoning. To probe the current understanding capabilities of computational models, we focus on generating generics exemplars --- specific cases when a generic holds true or false. In particular, we propose computational frameworks grounded in linguistic theory to generate the first datasets of exemplars. We then use our datasets to highlight the challenges generics pose for natural language reasoning and the current generic-understanding capabilities of large language models.

This thesis discusses the use of Bayesian Inference in inferring over the human's objective for Human-Robot Interaction, more specifically, it focuses upon the adaptation of methods to better utilize the information for inferring upon the human's objective for Reward Learning and Communicative Shared Autonomy settings. To accomplish this, we first examine state-of-the-art methods for approaching Bayesian Inverse Reinforcement learning where we explore the strengths and weaknesses of current approaches. After which we explore alternative methods for approaching the problem, borrowing similar approaches to those of the statistics community to apply alternative methods to improve the sampling process over the human's belief. After this, I then move to a discussion on the setting of Shared Autonomy in the presence and absence of communication. These differences are then explored in our method for inferring upon an environment where the human is aware of the robot's intention and how this can be used to dramatically improve the robot's ability to cooperate and infer upon the human's objective. In total, I conclude that the use of these methods to better infer upon the human's objective significantly improves the performance and cohesion between the human and robot agents within these settings. / Master of Science / This thesis discusses the use of various methods to allow robots to better understand human actions so that they can learn and work with those humans. In this work we focus upon two areas of inferring the human's objective: The first is where we work with learning what things the human prioritizes when completing certain tasks to better utilize the information inherent in the environment to best learn those priorities such that a robot can replicate the given task. The second body of work surrounds Shared Autonomy where we work to have the robot better infer what task a human is going to do and thus better allow the robot to assist with this goal through using communicative interfaces to alter the information dynamic the robot uses to infer upon that human intent. Collectively, the work of the thesis works to push that the current inference methods for Human-Robot Interaction can be improved through the further progression of inference to best approximate the human's internal model in a given setting.

The internet has served as the virtual world since the beginning of the digital era, and it has provided consumers the valuable source of information and become a fundamental basis of e-commerce by passing the limit of time and distance of offline stores. It is hard to imagine our life without the internet. Because consumers store and access their private and financial information on the internet, information security is even more important than ever. Although many studies demonstrate the importance of information security to consumers, researchers have paid little attention to consumers\' inference processing underlying their perceptions of information security. We investigate how consumers infer and evaluate online information security based on consumer inference making process and metacognitive experience. We argue that consumers\' perceived security could be enhanced by simply increasing complexity, even if that increased complexity is meaningless. It is because consumers have a belief that security is achieved by sacrificing convenience or increasing complexity. We demonstrated that consumers evaluated a website more secure when asked to enter redundant information in Chapter 1. Chapter 2 suggested that disfluency and difficulty of retrieval could increase perceived security because metacognitive experience makes consumers misattribute their feeling of difficulty to technical difficulty. We found that the positive effect of disfluency was held when a product was not security-related. In Chapter 3, we focused on how to improve the accuracy of security judgments. We found that perceived security enhanced by meaningless complexity would be adjusted by asking specific dimensions of security (Confidentiality, Integrity, and Availability), and the positive impact of a disfluency effect could be debiased by providing participants the true source of their subjective difficulty. Furthermore, we demonstrated that consumers\' interpretation about accessibility experience varied depending on what kind of naïve theory was activated. Through a series of experiments, we demonstrated our arguments were valid and these results provided useful insights and implications about consumers\' inference processing and perception of information security. / Ph. D.