Wang, Q. (STAT) – Modern Statistical Methods for Modeling Spatial and Temporal Processes

Modern scientific studies increasingly rely on complex datasets exhibiting spatial and temporal dependence, particularly in social, environmental, and climate applications. This dissertation develops statistical models and computational methods for analyzing such data, with an emphasis on capturing dependence structures, nonlinear dynamics, and uncertainty quantification.

A spatial deep learning framework is developed to extend classical geostatistical models by incorporating convolutional neural network architectures, allowing for flexible modeling of complex and nonstationary spatial dependence The proposed approach preserves principled uncertainty quantification alongside improved predictive performance for large and heterogeneous spatial datasets.

In the temporal domain, a Bayesian hierarchical echo state network model is introduced for count-valued time series, providing a flexible alternative to traditional autoregressive approaches. By embedding reservoir computing within a hierarchical probabilistic framework, the model accommodates nonlinear temporal dynamics while enabling coherent inference and uncertainty quantification, which are typically absent in standard neural network approaches.

Alongside these model-driven developments, we conduct a data-driven analysis of Northern Hemisphere snow cover using weekly satellite-derived observations from 1972 to 2024. A spatio-temporal modeling framework is developed that combines a seasonal two-state Markov structure for temporal dynamics with a Besag–York–Mollié (BYM) formulation to capture spatial dependence, allowing both trend and seasonal effects to vary across space. Covariates including temperature, latitude, and elevation are incorporated to explain observed patterns. The analysis reveals substantial spatial heterogeneity and pronounced seasonal structure, including week-specific trends and a coherent wave-like pattern of snow cover changes across continents.

Together, this thesis addresses key limitations of classical approaches to spatial and temporal data analysis, which often rely on restrictive assumptions that limit their ability to capture complex dependence structures and nonlinear dynamics. By integrating modern machine learning techniques with statistical modeling and complementing these developments with data-driven scientific analysis, this dissertation provides a flexible and principled framework for understanding complex spatio-temporal processes while maintaining uncertainty quantification.

Event Host: Qi Wang, Ph.D. Candidate, Statistical Science 

Advisor: Paul Parker

Zoom: https://ucsc.zoom.us/j/97486222296?pwd=419R7C5I6gLbbB0eLqwMcSVQLTN7bA.1

Passcode: 766602