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This dissertation focuses on estimation and selection methods for a simple linear model with two levels of variation. This model provides a foundation for extensions to more levels. We propose new regularization criteria for model selection, subset selection, and variable selection in this context. Regularization is a penalized-estimation approach that shrinks the estimate and selects variables for structured data. This dissertation introduces a procedure (HM-ALASSO) that extends regularized multilevel-model estimation and selection to enforce principles of fixed heredity (e.g., including main effects when their interactions are included) and random heredity (e.g., including fixed effects when their random terms are included). The goals in developing this method were to create a procedure that provided reasonable estimates of all parameters, adhered to fixed and random heredity principles, resulted in a parsimonious model, was theoretically justifiable, and was able to be implemented and used in available software. The HM-ALASSO incorporates heredity-constrained selection directly into the estimation process. HM-ALASSO is shown to enjoy the properties of consistency, sparsity, and asymptotic normality. The ability of HM-ALASSO to produce quality estimates of the underlying parameters while adhering to heredity principles is demonstrated using simulated data. The performance of HM-ALASSO is illustrated using a subset of the High School and Beyond (HS&B) data set that includes math-achievement outcomes modeled via student- and school-level predictors. The HM-ALASSO framework is flexible enough that it can be adapted for various rule sets and parameterizations. / Statistics

Model Driven Engineering (MDE) has gained a considerable attention in the software engineering domain in the past decade. MDE proposes shifting the focus of the engineers from concrete artifacts (e.g., code) to more abstract structures (i.e., models). Such a change allows using the human intelligence more efficiently in engineering software products. Model Transformation (MT) is one of the key operations in MDE and plays a critical role in its successful application. The current MT approaches, however, usually miss either one or both of the two essential features: 1) declarativity in the sense that the MT definitions should be expressed at a sufficiently high level of abstraction, and 2) formality in the sense that the approaches should be based on precise underlying semantics. These two features are both critical in effectively managing the complexity of a network of interrelated models in an MDE process. This thesis tackles these shortcomings by promoting a declarative MT approach that is built on mathematical foundations. The approach is called Query Structured Transformation (QueST) as it proposes a structured orchestration of diagrammatic queries in the MT definitions. The aim of the thesis is to make the QueST approach –that is based on formal foundations– accessible to the MDE community. This thesis first motivates the necessity of having declarative formal approaches by studying the variety of model synchronization scenarios in the networks of interrelated models. Then, it defines a diagrammatic query framework (DQF) that formulates the syntax and the semantics of the QueST collection-level diagrammatic operations. By a detailed comparison of the QueST approach and three rule-based MT approaches (ETL, ATL, and QVT-R), the thesis shows the way QueST contributes to the development of the following aspects of MT definitions: declarativity, modularity, incrementality, and logical analysis of MT definitions. / Thesis / Doctor of Philosophy (PhD)

Multivariate data is prevalent in modern applications, yet it often presents significant analytical challenges. Factor models can offer an effective tool to address issues associated with large-scale datasets. In this dissertation, we propose two novel Bayesian factors models. These models are designed to effectively reduce the dimensionality of the data, as the number of latent factors is typically much smaller than that of the observation vectors. Therefore, our proposed models can achieve substantial dimension reduction. Our first model is for spatiotemporal areal data. In this case, the region of interest is divided into subregions, and at each time point, there is one univariate observation per subregion. Our model writes the vector of observations at each time point in a factor model form as the product of a vector of factor loadings and a vector of common factors plus a vector of error. Our model assumes that the common factor evolves through time according to a dynamic linear model. To represent the spatial relationships among subregions, each column of the factor loadings matrix is assigned intrinsic conditional autoregressive (ICAR) priors. Therefore, we call our approach the Dynamic ICAR Spatiotemporal Factor Models (DIFM). Our second model, Bayesian Clustering Factor Model (BCFM) assumes latent factors and clusters are present in the data. We apply Gaussian mixture models on common factors to discover clusters. For both models, we develop MCMC to explore the posterior distribution of the parameters. To select the number of factors and, in the case of clustering methods, the number of clusters, we develop model selection criteria that utilize the Laplace-Metropolis estimator of the predictive density and BIC with integrated likelihood. / Doctor of Philosophy / Understanding large-scale datasets has emerged as one of the most significant challenges for researchers recently. This is particularly true for datasets that are inherently complex and nontrivial to analyze. In this dissertation, we present two novel classes of Bayesian factor models for two classes of complex datasets. Frequently, the number of factors is much smaller than the number of variables, and therefore factor models can be an effective approach to handle multivariate datasets. First, we develop Dynamic ICAR Spatiotemporal Factor Model (DIFM) for datasets collected on a partition of a spatial domain of interest over time. The DIFM accounts for the spatiotemporal correlation and provides predictions of future trends. Second, we develop Bayesian Clustering Factor Model (BCFM) for multivariate data that cluster in a space of dimension lower than the dimension of the vector of observations. BCFM enables researchers to identify different characteristics of the subgroups, offering valuable insights into their underlying structure.

Yes / A milk pasteurization process, a nonlinear process and multivariable interacting system, is difficult to control by the conventional on-off controllers since the on-off controller can handled the temperature profiles for milk and water oscillating over the plant requirements. The multi-variable control approach with model predictive control (MPC) is proposed in this study. The proposed algorithm was tested for control of a milk pasteurization process in three cases of simulation such as set point tracking, model mismatch, difference control and prediction horizons, and time sample. The results for the proposed algorithm show the well performance in keeping both the milk and water temperatures at the desired set points without any oscillation and overshoot and giving less drastic control action compared to the cascade generic model control (GMC) strategy.

Yes / Reverse osmosis process is used in many industrial applications ranging from solute-solvent to solvent-solvent and gaseous separation. A number of theoretical models have been developed to describe the separation and fluxes of solvent and solute in such processes. This paper looks into the scope and limitations of two main models (the irreversible thermodynamics and the solution diffusion models) used in the past by several researchers for solute-solvent feed separation. Despite the investigation of other complex models, the simple concepts of these models accelerate the feasibility of the implementation of reverse osmosis for different types of systems and variety of industries. Briefly, an extensive review of these mathematical models is conducted by collecting more than 70 examples from literature in this study. In addition, this review has covered the improvement of such models to make them compatible with multi-component systems with consideration of concentration polarization and solvent-solute-membrane interaction.

This research is motivated by an issue frequently encountered in water quality monitoring and ecological assessment. One concern for researchers and watershed resource managers is how the biological community in a watershed is affected by human activities. The conventional single model approach based on regression and logistic regression usually fails to adequately model the relationship between biological responses and environmental stressors since the study samples are collected over a large spatial region and the response-stressor relationships are usually weak in this situation. In this dissertation, we propose two alternative modeling approaches to partition the whole region of study into disjoint subregions and model the response-stressor relationships within subregions simultaneously. In our examples, these modeling approaches found stronger relationships within subregions and should help the resource managers improve impairment assessment and decision making. The first approach is an adjusted Bayesian classification and regression tree (ABCART). It is based on the Bayesian classification and regression tree approach (BCART) and is modified to accommodate spatial partitions in ecological studies. The second approach is a Voronoi diagram based partition approach. This approach uses the Voronoi diagram technique to randomly partition the whole region into subregions with predetermined minimum sample size. The optimal partition/cluster is selected by Monte Carlo simulation. We propose several model selection criteria for optimal partitioning and modeling according to the nature of the study and extend it to multivariate analysis to find the underlying structure of response-stressor relationships. We also propose a multivariate hotspot detection approach (MHDM) to find the region where the response-stressor relationship is the strongest according to an R-square-like criterion. Several sets of ecological data are studied in this dissertation to illustrate the implementation of the above partition modeling approaches. The findings from these studies are consistent with other studies. / Ph. D.

Coarse woody debris (CWD) plays an influential role in forested ecosystems by adding organic matter to soils, stabilizing the soil environment, providing wildlife habitat, preventing soil erosion, providing seedling establishment habitat, and involvement in the nutrient cycle. Most CWD research has been conducted in old-growth and unmanaged, second-growth forests. However, less is understood about CWD in intensively managed ecosystems, such as industrialized southern pine plantations. The objectives of this study were to determine the climatic and ecological factors that affect the decomposition rate of CWD, to predict the decomposition rate, specific gravity, and time since death (TSD) using multiple linear regression in industrial loblolly pine (Pinus taeda L.) plantations in the southeastern United States. The study sites for this project were part of a long-term, loblolly pine thinning study maintained by the Loblolly Pine Growth and Yield Research Cooperative at Virginia Tech. Measurements included piece size, position, and decay class. Samples of CWD were collected and analyzed to determine their mass and density. Decomposition rate of CWD was significantly different across position classes and decay classes: disk decomposition rates were significantly negatively correlated with disk diameter, large and small end piece diameter, estimated disk height, and disk dry weight. Average annual precipitation and average annual temperature were not significantly correlated with CWD disk decomposition rate. / Master of Science

A recent trend in education has been toward formative assessments to enable teachers, parents, and administrators assist students succeed. Cognitive diagnostic modeling (CDM) has the potential to provide valuable information for stakeholders to assist students identify their skill deficiency in specific academic subjects. Cognitive diagnosis models are mainly viewed as a family of latent class confirmatory probabilistic models. These models allow the mapping of students' skill profiles/academic ability. Using a complex simulation studies, the methodological issues in one of the existing cognitive models, referred to as compensatory reparameterized unified model (CRUM) under the log-linear model family of CDM, was investigated. In order for practitioners to implement these models, their item parameter recovery and examinees' classifications need to be studied in detail. A series of complex simulated data were generated for investigation with the following designs: three attributes with seven items, three attributes with thirty five items, four attributes with fifteen items, and five attributes with thirty one items. Each dataset was generated with observations of: 50, 100, 500, 1,000, 5,000, and 10,000 examinees. The first manuscript is the report of the investigation of how accurately CRUM could recover item parameters and classify examinees under true QMattrix specification and various research designs. The results suggested that the test length with regards to number of attributes and sample size affects the item parameter recovery and examinees classification accuracy. The second manuscript is the report of the investigation of the sensitivity of relative fit indices in detecting misfit for over- and opposite-Q-Matrix misspecifications. The relative fit indices under investigation were Akaike information criterion (AIC), Bayesian information criterion (BIC), and sample size adjusted Bayesian information criterion (ssaBIC). The results suggested that the CRUM can be a robust model given the consideration to the observation number and item/attribute combinations. The findings of this dissertation fill some of the existing gaps in the methodological issues regarding cognitive models' applicability and generalizability. It helps practitioners design tests in CDM framework in order to attain reliable and valid results. / Ph. D.

The cell cycle of budding yeast is controlled by a complex chemically reacting network of a large group of species, including mRNAs and proteins. Many mathematical models have been proposed to unravel its molecular mechanism. However, it is hard for people with less training to visually interpret the dynamics from the simulation results of these models. In this thesis, we use the visualization toolkit D3 and jQuery to design a web-based interface and help users to visualize the cell cycle simulation results. It is essentially a website where the proliferation of the wild-type and mutant cells can be visualized as dynamical animation. With the help of this visualization tool, we can easily and intuitively see many key steps in the budding yeast cell cycle procedure, such as bud emergence, DNA synthesis, mitosis, cell division, and the current populations of species. / Master of Science / The cell cycle of budding yeast is controlled by a complex chemically reacting network. Many mathematical models have been proposed to unravel its molecular mechanism. However, it is hard to visually interpret the dynamics from the simulation results of these models. In this thesis, we use the visualization toolkit D3 and jQuery to design a web-based interface and help users to visualize the cell cycle simulation results. It is essentially a webpage where the proliferation of the wild-type and mutant cells can be visualized as dynamical animation.