Bayesian hierarchical modeling and its applications to clustering and data privacy preservation
Creators: Yu, Peng
Publisher: name: University of Alberta Library
Year: 2024

<p>The evolution of data acquisition technologies and the exponential growth in computing capabilities have inaugurated an epoch wherein researchers are empowered to procure data of unprecedented dimensionality and complexity. Simultaneously, Bayesian hierarchical models distinguish themselves as promising methodologies, offering versatile frameworks for modeling and addressing intricate data-driven challenges. This thesis harnesses the power of this advanced Bayesian statistical framework to explore innovative solutions in the realms of neuroimaging data interpretation, mental health assessment, and differentially private data analysis. The work is organized into three distinct parts, each dedicated to a specific application of Bayesian hierarchical modeling, reflecting its capacity to tackle diverse analytical problems. The first section of the thesis concentrates on the analysis of electroencephalogram (EEG) data, leveraging Bayesian hierarchical models to uncover latent structures and patterns within the complex signals. This part introduces a groundbreaking approach to EEG data analysis, emphasizing the model&#39;s ability to discern intricate neural activity patterns that elude traditional analysis techniques. By applying this novel methodology to EEG datasets, the study not only demonstrates the model&#39;s superior analytical prowess but also highlights its potential to revolutionize our understanding of neural dynamics, offering new insights into brain function and disorder diagnostics. In the second segment, attention shifts to the Hamilton Depression Rating Scale (HAMD), a widely recognized metric for assessing depression severity. Here, Bayesian hierarchical models are employed to analyze HAMD data, aiming to identify latent subgroups among patients and predict treatment outcomes more accurately. This section showcases the application of the model to clinical trial data, revealing its capability to enhance the precision of depression severity assessment and to inform personalized treatment strategies. The use of Bayesian hierarchical models in this context exemplifies the model&#39;s adaptability and its potential to contribute meaningfully to the field of mental health. The final part of the thesis addresses the critical issue of data privacy, particularly through the lens of differential privacy (DP). It presents an innovative integration of DP principles within the Bayesian hierarchical modeling framework to safeguard individual privacy in data analysis. This approach not only demonstrates a novel method for achieving privacy-preserving but also improves the efficiency of the statistical inference. By weaving together these diverse applications—ranging from EEG data analysis and mental health assessment to privacy preservation—the thesis underscores the versatility and power of Bayesian hierarchical modeling. Each section, grounded in rigorous theoretical derivations and validated through extensive simulations and real-data applications, contributes to the advancement of statistical analysis in its respective field. Collectively, this thesis not only enriches our understanding of Bayesian hierarchical modeling but also opens new avenues for research and application of Bayesian hierarchical models in neuroscience, mental health, and data privacy.</p>