Subject Area
Statistics
Abstract
This dissertation addresses two distinct topics related to count time series analysis and topological medical image analysis, respectively. The first part of the dissertation comprises an application of a count time series model to analysis of US monthly sex trafficking data and development of a new model for multivariate count data that exhibits serial dependence and overdispersion. By imposing a family of multivariate mixed Poisson distributions on the count random vector, the proposed model can accommodate a broad range of overdispersion as well as positive contemporaneous correlations. For maximum likelihood estimation, a computationally feasible EM-type algorithm is derived based on the stochastic construction of mixed Poisson distributions. To address these challenges computational burdens stemming from non-closed-form expectations in the E-step and nested numerical optimization in the M-step, Monte Carlo integration and the generalized EM (GEM) principle are additionally adopted. The second part of this dissertation is dedicated to extracting persistent homology-based topological features from medical images for prognostic survival analysis. We present two comprehensive case studies involving patients with glioblastoma (GBM) and lung adenocarcinoma (LUAD). For the GBM study, we propose applying persistent homology to the signed distance-transformed images of AI-segmented brain MRI scans. Smoothed persistence diagrams are then computed to characterize the compositional shape patterns of tumor lesions, thereby capturing prognostic information for survival outcomes. In the LUAD study, we topologically quantify the spatial alignment among cellular components identified in AI-segmented hematoxylin and eosin (H&E)-stained images. In contrast to the GBM study, we utilize cumulative persistence curves as a simpler, yet highly informative, functional summary of persistence distributions rather than directly smoothing the persistence diagrams. For both applications, the persistence outputs are represented as functional data to integrate them into downstream statistical modeling. Our results demonstrate that the proposed topological features improve prognostic performance in survival outcome prediction.
Degree Date
Summer 8-4-2026
Document Type
Dissertation
Degree Name
Ph.D.
Department
Department of Statistics and Data Science
Advisor
Chul Moon
Second Advisor
Raanju Sundararajan
Format
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License
Recommended Citation
Jang, Yuhyeong, "Statistical Methodologies For Count Time Series Analysis and Topological Data Analysis of Medical Images" (2026). Statistical Science Theses and Dissertations. 58.
https://scholar.smu.edu/hum_sci_statisticalscience_etds/58
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