Slovenia became an independent republic with its own constitution passed on December 23, 1991. The important step that led to the independence of Slovenia was the December 1990 plebiscite. It was at this plebiscite that the citizens of Slovenia voted for a sovereign and independent state. A public survey called Slovenian Public Opinion (SPO) survey was taken by the government of Slovenia for the plebiscite. The plebiscite counted `YES voters' only those voters who attended and who voted for independence. Non-voters were counted as `NO voters' and `Don't Know' survey responses that could be thought of as missing data that was treated as `YES' or `NO'. Analysis of survey data is done using non-parametric fitting procedure, Bayesian ignorable nonresponse model and Bayesian nonignorable nonresponse model. Finally, a sensitivity analysis is conducted with respect to the different values of a prior parameter. The amazing estimates of the eventual plebiscite outcome show the validity our underlying models.

Bayesian statistical methods have long been computationally out of reach because the analysis often requires integration of high-dimensional functions. Recent advancements in computational tools to apply Markov Chain Monte Carlo (MCMC) methods are making Bayesian data analysis accessible for all statisticians. Two such computer tools are Win-BUGS and SASR 9.2's PROC MCMC. Bayesian methodology will be introduced through discussion of fourteen statistical examples with code and computer output to demonstrate the power of these computational tools in a wide variety of settings.

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Clinical intelligence about a patient's risk of future adverse health events can support clinical decision making in personalized and preventive care. Healthcare predictive analytics using electronic health records offers a promising direction to address the challenging tasks of risk profiling. Patients with chronic diseases often face risks of not just one, but an array of adverse health events. However, existing risk models typically focus on one specific event and do not predict multiple outcomes. To attain enhanced risk profiling, we adopt the design science paradigm and propose a principled approach called Bayesian multitask learning (BMTL). Considering the model development for an event as a single task, our BMTL approach is to coordinate a set of baseline models-one for each event-and communicate training information across the models. The BMTL approach allows healthcare providers to achieve multifaceted risk profiling and model an arbitrary number of events simultaneously. Our experimental evaluations demonstrate that the BMTL approach attains an improved predictive performance when compared with the alternatives that model multiple events separately. We also find that, in most cases, the BMTL approach significantly outperforms existing multitask learning techniques. More importantly, our analysis shows that the BMTL approach can create significant potential impacts on clinical practice in reducing the failures and delays in preventive interventions. We discuss several implications of this study for health IT, big data and predictive analytics, and design science research.

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Mathematical probability has a rich theory and powerful applications. Of particular note is the Markov chain Monte Carlo (MCMC) method for sampling from high dimensional distributions that may not admit a naive analysis. We develop the theory of the MCMC method from first principles and prove its relevance. We also define a Bayesian hierarchical model for generating data. By understanding how data are generated we may infer hidden structure about these models. We use a specific MCMC method called a Gibbs' sampler to discover topic distributions in a hierarchical Bayesian model called Topics Over Time. We propose an innovative use of this model to discover disease and treatment topics in a corpus of health insurance claims data. By representing individuals as mixtures of topics, we are able to consider their future costs on an individual level rather than as part of a large collective.

<div><b>1. A Closed-Loop Machine Learning and Compensation Framework for Geometric Accuracy Control of 3D Printed Products</b></div><div><b><br></b></div>Additive manufacturing (AM) systems enable direct printing of three-dimensional (3D) physical products from computer-aided design (CAD) models. Despite the many advantages that AM systems have over traditional manufacturing, one of their significant limitations that impedes their wide adoption is geometric inaccuracies, or shape deviations between the printed product and the nominal CAD model. Machine learning for shape deviations can enable geometric accuracy control of 3D printed products via the generation of compensation plans, which are modifications of CAD models informed by the machine learning algorithm that reduce deviations in expectation. However, existing machine learning and compensation frameworks cannot accommodate deviations of fully 3D shapes with different geometries. The feasibility of existing frameworks for geometric accuracy control is further limited by resource constraints in AM systems that prevent the printing of multiple copies of new shapes.<div><br></div><div>We present a closed-loop machine learning and compensation framework that can improve geometric accuracy control of 3D shapes in AM systems. Our framework is based on a Bayesian extreme learning machine (BELM) architecture that leverages data and deviation models from previously printed products to transfer deviation models, and more accurately capture deviation patterns, for new 3D products. The closed-loop nature of compensation under our framework, in which past compensated products that do not adequately meet dimensional specifications are fed into the BELMs to re-learn the deviation model, enables the identification of effective compensation plans and satisfies resource constraints by printing only one new shape at a time. The power and cost-effectiveness of our framework are demonstrated with two validation experiments that involve different geometries for a Markforged Metal X AM machine printing 17-4 PH stainless steel products. As demonstrated in our case studies, our framework can reduce shape inaccuracies by 30% to 60% (depending on a shape's geometric complexity) in at most two iterations, with three training shapes and one or two test shapes for a specific geometry involved across the iterations. We also perform an additional validation experiment using a third geometry to establish the capabilities of our framework for prospective shape deviation prediction of 3D shapes that have never been printed before. This third experiment indicates that choosing one suitable class of past products for prospective prediction and model transfer, instead of including all past printed products with different geometries, could be sufficient for obtaining deviation models with good predictive performance. Ultimately, our closed-loop machine learning and compensation framework provides an important step towards accurate and cost-efficient deviation modeling and compensation for fully 3D printed products using a minimal number of printed training and test shapes, and thereby can advance AM as a high-quality manufacturing paradigm.<br></div><div><br></div><div><b>2. Multiple Imputation and the Bootstrap for the Analysis of Big Data with Missingness</b></div><div><br></div><div>Inference can be a challenging task for Big Data. Two significant issues are that Big Data frequently exhibit complicated missing data patterns, and that the complex statistical models and machine learning algorithms typically used to analyze Big Data do not have convenient quantification of uncertainties for estimators. These two difficulties have previously been addressed using multiple imputation and the bootstrap, respectively. However, it is not clear how multiple imputation and bootstrap procedures can be effectively combined to perform statistical inferences on Big Data with missing values. We investigate a practical framework for the combination of multiple imputation and bootstrap methods. Our framework is based on two principles: distribution of multiple imputation and bootstrap calculations across parallel computational cores, and the quantification of sources of variability involved in bootstrap procedures that use subsampling techniques via random effects or hierarchical models. This framework effectively extends the scope of existing methods for multiple imputation and the bootstrap to a broad range of Big Data settings. We perform simulation studies for linear and logistic regression across Big Data settings with different rates of missingness to characterize the frequentist properties and computational efficiencies of the combinations of multiple imputation and the bootstrap. We further illustrate how effective combinations of multiple imputation and the bootstrap for Big Data analyses can be identified in practice by means of both the simulation studies and a case study on COVID infection status data. Ultimately, our investigation demonstrates how the flexible combination of multiple imputation and the bootstrap under our framework can enable valid statistical inferences in an effective manner for Big Data with missingness.<br></div>