<p dir="ltr">In recent years, probabilistic graphical models have emerged as a powerful framework for understanding complex dependencies in multivariate data, offering a structured approach to tackle uncertainty and model complexity. These models have revolutionized the way we interpret the interplay between variables in various domains, from genetics to social network analysis. Inspired by the potential of probabilistic graphical models to provide insightful data analysis while addressing the challenges of high-dimensionality and computational efficiency, this dissertation introduces two novel methodologies that leverage the strengths of graphical models in high-dimensional settings. By integrating advanced inference techniques and exploiting the structural advantages of graphical models, we demonstrate how these approaches can efficiently decode complex data patterns, offering significant improvements over traditional methods. This work not only contributes to the theoretical advancements in the field of statistical data analysis but also provides practical solutions to real-world problems characterized by large-scale, complex datasets.</p><p dir="ltr">Firstly, we introduce a novel Bayesian hybrid method for learning the structure of Gaus- sian Bayesian Networks (GBNs), addressing the critical challenge of order determination in constraint-based and score-based methodologies. By integrating a permutation matrix within the likelihood function, we propose a technique that remains invariant to data shuffling, thereby overcoming the limitations of traditional approaches. Utilizing Cholesky decompo- sition, we reparameterize the log-likelihood function to facilitate the identification of the parent-child relationship among nodes without relying on the faithfulness assumption. This method efficiently manages the permutation matrix to optimize for the sparsest Cholesky factor, leveraging the Bayesian Information Criterion (BIC) for model selection. Theoretical analysis and extensive simulations demonstrate the superiority of our method in terms of precision, recall, and F1-score across various network complexities and sample sizes. Specifically, our approach shows significant advantages in small-n-large-p scenarios, outperforming existing methods in detecting complex network structures with limited data. Real-world applications on datasets such as ECOLI70, ARTH150, MAGIC-IRRI, and MAGIC-NIAB further validate the effectiveness and robustness of our proposed method. Our findings contribute to the field of Bayesian network structure learning by providing a scalable, efficient, and reliable tool for modeling high-dimensional data structures.</p><p dir="ltr">Secondly, we introduce a Bayesian methodology tailored for Gaussian Graphical Models (GGMs) that bridges the gap between GBNs and GGMs. Utilizing the Cholesky decomposition, we establish a novel connection that leverages estimated GBN structures to accurately recover and estimate GGMs. This innovative approach benefits from a theoretical foundation provided by a theorem that connects sparse priors on Cholesky factors with the sparsity of the precision matrix, facilitating effective structure recovery in GGMs. To assess the efficacy of our proposed method, we conduct comprehensive simulations on AR2 and circle graph models, comparing its performance with renowned algorithms such as GLASSO, CLIME, and SPACE across various dimensions. Our evaluation, based on metrics like estimation ac- curacy and selection correctness, unequivocally demonstrates the superiority of our approach in accurately identifying the intrinsic graph structure. The empirical results underscore the robustness and scalability of our method, underscoring its potential as an indispensable tool for statistical data analysis, especially in the context of complex datasets.</p>

Domain Specific Modeling (DSM) aims to increase productivity of software development by raising the level of abstraction beyond code concepts and using domain concepts. By providing a generative model-driven tooling component and runtime support, the Eclipse Graphical Modeling Framework (GMF) aims to simplify the creation of diagram editors for specific domains based on a series of model creation and transformation steps. GMF leverages the Eclipse Modeling Framework (EMF) and the Eclipse Graphical Editing Framework (GEF) to allow the graphical modeling of Domain Specific Languages (DSL). A Domain Specific Language (DSL) is developed specifically for a specific task and specific domain. In this research, the State Machine Compiler (SMC) represents the specific domain for which a DSL in a form of a diagram editor is developed using GMF. SMC is an open source Java tool allowing generation of state pattern classes from textual descriptions of state machines. The main objective of this research is to describe the use of GMF, highlight potential pitfalls and identify strengths and weaknesses of GMF based on certain criteria. To be able to feed the SMC diagrams created with the editor into SMC, a Java Emitter Templates (JET) transformation is used to transform SMC model instances into textual format expected by SMC. / Thesis (Master, Computing) -- Queen's University, 2011-04-14 18:58:08.797

This paper deals with the creation of the tool for chip design in UML. The intention of this work is to present the news in the UML language version 2.0, that can be possibly used for modeling of embedded systems. Furthermore, it deals with the possibility and method of modeling in the Eclipse environment and it focuses on the Eclipse Modeling Framework. This work explains the principle of developing of graphical editors based on GMF used fully by developing tool. Finally, it discusses the chosen solution.