The human body is an incredibly complex system that researchers have studied for decades to uncover its secrets. Genetic, transcriptomic, and epigenetic data each offer unique insights into its functioning. Recent technological advancements have enabled the generation of vast amounts of high-quality biological data, creating unprecedented opportunities to explore molecular mechanisms underlying health and disease. Analyzing these diverse datasets is crucial for developing targeted therapies, personalized medicine, and advancing our understanding of biology. Building advanced statistical and computational models to handle these complex datasets is now more important than ever for translating biological information into actionable insights and driving breakthroughs in medical research and treatment strategies. In this dissertation, I first developed BayesKAT, a kernel-based testing methodology for assessing the association between user-defined groups of SNPs or genes and a phenotype of interest (Chapter 2). Unlike existing kernel-based tests that use predefined single or average kernels and often yield ambiguous results, this algorithm adaptively selects the optimal composite kernel using a Gaussian process model within a Bayesian framework, providing more interpretable outcomes. Next, I explored the emerging field of spatial transcriptomics, where similar Gaussian process models and kernel-based testing have significant potential. To complement the recent surge in spatial transcriptomics research, Chapter 3 presents a comprehensive literature review of significant methodologies, particularly for spatial gene detection, which is a crucial step in spatial transcriptomics data analysis. This review provides an overview of the current state of research in the field. In Chapter 4, I extended the kernel-based testing procedure to address challenges in spatial transcriptomic data. The newly developed algorithm, cSVG, not only detects spatially variable genes, but also improves spatial domain detection accuracy and addresses additional problems in this field. Finally, to tackle the scarcity of crucial TF binding information for many transcription factors (TFs) across various cell types, I developed a computational model, 3D-TF-IMPUTE (Chapter 5). This model predicts TF binding sites by utilizing readily available epigenetic datasets and leveraging the three-dimensional structure of the genome in an unsupervised manner, efficiently predicting TF binding sites essential for understanding the functional genome. By tackling key challenges in the analysis of genetic, transcriptomic, and epigenetic data, this dissertation makes significant contributions to the field. It provides powerful tools for researchers to better understand the molecular underpinnings of health and disease, paving the way for future breakthroughs in biomedical research.
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