The International Normalizing Ratio (INR) measures the speed at which blood clots. Healthy people have an INR of about one. Some people are at greater risk of blood clots and their physician prescribes a target INR range, generally 2-3. The farther a patient is above or below their prescribed range, the more dangerous their situation. A variety of point-of-care (POC) devices has been developed to monitor patients. The purpose of this research was to develop innovative graphics to help describe a highly unbalanced dataset and to carry out Bayesian analyses to determine which of five devices best manages patients. An initial Bayesian analysis compared a machine-identical beta-binomial model to a machine-specific beta-binomial model. The response variable was number of in-range visits. A second Bayesian analysis compared a machine-identical lognormal model, a machine-specific lognormal model, and a machine-specific lognormal model with lower therapeutic bound as a predictor. The response variable was INR. Machines were compared using posterior predictive distributions of the absolute distance outside a patient's therapeutic range. For the beta-binomial models, the machine-identical model had the lower DIC, meaning that POC device was not a strong predictor of success in keeping a patient in-range. The machine-specific lognormal model with a term for lower therapeutic bound had the lowest DIC of the three lognormal models, implying that the additional information of distance out of range revealed differences among the POC devices. Three of the machines had more favorable out-of-range distributions than the other two. Both Bayesian analyses provided useful information for medical practice in managing INR.

University students often complete evaluations of their courses and instructors. The evaluation tool typically contains questions about the course and the instructor on an ordinal Likert scale. We assess instructor effectiveness while adjusting for known confounders. We present a probit regression model with a latent variable to measure the instructor effectiveness accounting for student specific covariates, such as student grade in the course, high school and university GPA, and ACT score.

Many problems of design and operation in science and engineering can be formulated as optimization of a properly defined performance/objective function over a design space. This thesis considers optimization problems where information about the performance function can be obtained only through experimentation/function evaluation, in other words, optimization of black box functions. Furthermore, it is assumed that the optimization is performed with limited budget, namely, where only a limited number of function evaluations are feasible. Two classes of optimization approaches are considered. The first, consisting of Design of Experiment (DOE) and Response Surface Methodology (RSM), explores the design space locally by identifying directions of improvement and incrementally moving towards the optimum. The second, referred to as Bayesian Optimization (BO), corresponds to a global search of the design space based on a stochastic model of the function over the design space that is updated after each experimentation/function evaluation. Two independent projects related to the above optimization approaches are reported in the thesis. The first, the result of a collaborative effort with experimental and computational material scientists, involves adaptations of the above approaches in order to solve two specific new materials development projects. The goal of the first project was to develop an integrated computational-statistical-experimental methodology for calibration of an activated carbon adsorption bed. The second project consisted of the application and modification of existing DOE approaches to a highly data limited environment. The second part consists of a new contribution to the methodology of Bayesian Optimization (BO) by significantly generalizing a non-myopic approach to BO. Different BO algorithms vary based on their choice of stochastic model of the unknown objective function, referred to as the surrogate model, and that of the so-called acquisition function, which often represents an expected utility of sampling at various points of the design space. Various myopic BO approaches which evaluate the benefit of taking only a single sample from the objective function have been considered in the literature. More recently, a number of non-myopic approaches have been proposed that go beyond evaluating the benefit of a single sample. In this thesis, a non-myopic approach/algorithm, referred to as z* policy, is considered that takes a different approach to evaluating the benefits of sampling. The resulting search approach is motivated by a non-myopic index policy in a sequential sampling problem that is shown to be optimal in a non-adaptive setting. An analysis of the z* policy is presented and it is placed within the broader context of non-myopic policies. Finally, using empirical evaluations, it is shown that in some instances the z* policy outperforms a number of other commonly used myopic and non-myopic policies. / 2023-11-30T00:00:00Z

Bayesian model selection is a useful tool for identifying an appropriate model class, dependence structure, and valuable predictors for a wide variety of applications. In this work we consider objective Bayesian model selection where no subjective information is available to inform priors on model parameters a priori, specifically in the case of hierarchical models for spatial data, which can have complex dependence structures. We develop an approach using trained priors via fractional Bayes factors where standard Bayesian model selection methods fail to produce valid probabilities under improper reference priors. This enables researchers to concurrently determine whether spatial dependence between observations is apparent and identify important predictors for modeling the response. In addition to model selection with objective priors on model parameters, we also consider the case where the priors on the model space are used to penalize individual predictors a priori based on their costs. We propose a flexible approach that introduces a tuning parameter to cost-penalizing model priors that allows researchers to control the level of cost penalization to meet budget constraints and accommodate increasing sample sizes. / Doctor of Philosophy / Spatial data, such as data collected over a geographic region, is relevant in many fields. Spatial data can require complex models to study, but use of these models can impose unnecessary computations and increased difficulty for interpretation when spatial dependence is weak or not present. We develop a method to simultaneously determine whether a spatial model is necessary to understand the data and choose important variables associated with the outcome of interest. Within a class of simpler, linear models, we propose a technique to identify important variables associated with an outcome when there exists a budget or general desire to minimize the cost of collecting the variables.

In a Bayesian perspective, the probabilistic dependencies between hypotheses under consideration and diagnostic pieces of evidence are the only relevant information for probabilistic updating. We investigated whether human probability judgments conform to this assumption, by manipulating the sensory systems involved in the acquisition and processing of information concerning evidence and hypotheses. Hence, we ran five (computer-based) experiments using a variant of the classic book bag and poker chip task (e.g., Phillips & Edwards, 1966). Participants were first presented with pairs of urns A and B filled with a different proportion of balls that turned either red or green in the visual condition, balls that emitted either a low- or high-pitched sound in the auditory condition, and balls that both turned a color and emitted a sound in various cross-modal (i.e., audio-visual) conditions. One urn was then selected at random, some balls were randomly drawn from it, and their color and/or sound were disclosed. Participants’ task was to estimate the probability that each of the two urns has been selected, given the information provided. In Experiments 1 and 2, we compared the probability judgments referring to probabilistically identical visual and auditory scenarios that only differed with regards to the sensory system involved, without finding any difference between the answers provided in the two conditions. In Experiment 3, 4, and 5, the addition of cross-modal scenarios allowed us to investigate the effects on probabilistic updating of synergic (i.e., both visual and auditory evidence individually supported the hypothesis they jointly supported) or contrasting (i.e., either visual and/or auditory evidence individually supported the hypothesis opposite the one they jointly supported) audio-visual evidence. Our results provide evidence in favor of a synergy-contrasting effect, as probability judgments were more accurate in synergic conditions than in contrasting conditions. This suggests that, when perceptual information is acquired through a singular sensory system, probability judgments conform to the Bayesian assumption that the sensory system involved does not play a role in the updating process, whereas the simultaneous presentation of cross-modal information can influence participants’ performance.

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Supply chains are complex systems. Researchers in the Social and Decision Analytics Laboratory (SDAL) at Virginia Tech worked with a major global supply chain company to simulate an end-to-end supply chain. The supply chain data includes raw materials, production lines, inventory, customer orders, and shipments. Including contributions of this author, Pires, Sabin, Higdon et al. (2017) developed simulations for the production, customer orders, and shipments. Customer orders are at the center of understanding behavior in a supply chain. This dissertation continues the supply chain simulation work by improving the order simulation. Orders come from a diverse set of customers with different habits. These habits can differ when it comes to which products they order, how often they order, how spaced out those orders times are, and how much of each of those products are ordered. This dissertation is unique in that it relies extensively on Dirichlet and multiscale methods to tackle supply-chain order simulation. Multiscale model methodology is furthered to include Dirichlet models which are used to simulate order times for each customer and the collective system on different scales. / Doctor of Philosophy / This dissertation continues the supply chain simulation work of researchers (Pires et al. (2017)) in the Social and Decision Analytics Laboratory (SDAL) at Virginia Tech by improving the order simulation. Orders come from a diverse set of customers with different habits. These habits can di er when it comes to which products they order, how often they order, how spaced out those orders times are, and how much of each of those products are ordered. This dissertation is unique from the previous work at SDAL which considered few of these factors in order simulation and introduces statistical methodologies to deal with the complex nature of simulating an entire supply chain's orders.