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.

Forestry in the UK is dominated by coniferous plantations. Sitka spruce (Picea sitchensis) and Scots pine (Pinus sylvestris) are the most prevalent species and are mostly grown in single age mono-culture stands. Forest strategy for Scotland, England, and Wales all include efforts to achieve further afforestation. The aim of this afforestation is to provide a multi-functional forest with a broad range of benefits. Due to the time scale involved in forestry, accurate forecasts of stand productivity (along with clearly defined uncertainties) are essential to forest managers. These can be provided by a range of approaches to modelling forest growth. In this project model comparison, Bayesian calibration, and data assimilation methods were all used to attempt to improve forecasts and understanding of uncertainty therein of the two most important conifers in UK forestry. Three different forest growth models were compared in simulating growth of Scots pine. A yield table approach, the process-based 3PGN model, and a Stand Level Dynamic Growth (SLeDG) model were used. Predictions were compared graphically over the typical productivity range for Scots pine in the UK. Strengths and weaknesses of each model were considered. All three produced similar growth trajectories. The greatest difference between models was in volume and biomass in unthinned stands where the yield table predicted a much larger range compared to the other two models. Future advances in data availability and computing power should allow for greater use of process-based models, but in the interim more flexible dynamic growth models may be more useful than static yield tables for providing predictions which extend to non-standard management prescriptions and estimates of early growth and yield. A Bayesian calibration of the SLeDG model was carried out for both Sitka spruce and Scots pine in the UK for the first time. Bayesian calibrations allow both model structure and parameters to be assessed simultaneously in a probabilistic framework, providing a model with which forecasts and their uncertainty can be better understood and quantified using posterior probability distributions. Two different structures for including local productivity in the model were compared with a Bayesian model comparison. A complete calibration of the more probable model structure was then completed. Example forecasts from the calibration were compatible with existing yield tables for both species. This method could be applied to other species or other model structures in the future. Finally, data assimilation was investigated as a way of reducing forecast uncertainty. Data assimilation assumes that neither observations nor models provide a perfect description of a system, but combining them may provide the best estimate. SLeDG model predictions and LiDAR measurements for sub-compartments within Queen Elizabeth Forest Park were combined with an Ensemble Kalman Filter. Uncertainty was reduced following the second data assimilation in all of the state variables. However, errors in stand delineation and estimated stand yield class may have caused observational uncertainty to be greater thus reducing the efficacy of the method for reducing overall uncertainty.

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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Segmentation of human head on medical images is an important process in a wide array of applications such as diagnosis, facial surgery planning, prosthesis design, and forensic identification. In this study, a new Bayesian method for segmentation of facial tissues is presented. Segmentation classes include muscle, bone, fat, air and skin. The method incorporates a model to account for image blurring during data acquisition, a prior helping to reduce noise as well as a partial volume model. Regularization based on isotropic and directional Markov Random Field priors are integrated to the algorithm and their effects on segmentation accuracy are investigated. The Bayesian model is solved iteratively yielding tissue class labels at every voxel of an image. Sub-methods as variations of the main method are generated by switching on/off a combination of the models. Testing of the sub-methods are performed on two patients using single modality three-dimensional (3D) images as well as registered multi-modal 3D images (Magnetic Resonance and Computerized Tomography). Numerical, visual and statistical analyses of the methods are conducted. Improved segmentation accuracy is obtained through the use of the proposed image models and multi-modal data. The methods are also compared with the Level Set method and an adaptive Bayesiansegmentation method proposed in a previous study.

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.