Spatio-Temporal Statistical Inference for Human Mobility Using GPS Data

Abstract

Understanding where individuals spend their time over space and time is a central question in the study of human mobility. The increasing availability of high-resolution GPS data provides unprecedented opportunities to address this question, but also poses substantial statistical challenges arising from measurement error, heterogeneous sampling frequencies, and complex temporal structure. This dissertation develops a unified spatio-temporal statistical framework for modeling and estimating interpretable summaries of long-term human mobility from GPS data. At the core of the framework is a stochastic representation of daily mobility patterns, in which GPS observations are viewed as noisy measurements of latent spatio-temporal movement processes. Within this data-generating view, key inferential targets are formulated as time-allocation functionals that quantify the proportion of time individuals spend in different spatial regions. Estimation procedures are constructed by combining time-weighted representations of observed locations with aggregation across days, yielding activity-related summaries with well-defined statistical properties. This approach shifts attention from trajectory reconstruction to the principled estimation of time allocation over space. The central inferential construct emerging from this modeling strategy is the activity space, defined as a time-weighted characterization of routine spatial behavior. Rather than treating movement paths as primary objects of analysis, activity spaces are derived as functionals of latent daily processes, allowing for coherent inference under realistic measurement conditions. The framework accommodates multiple spatial supports, including continuous domains, geometrically constrained environments, and aggregated regional contexts. The dissertation consists of three complementary main chapters. Chapter 2 establishes the foundational modeling and estimation framework for daily mobility processes and derives statistical properties for time-proportion estimators. Chapter 3 extends this framework to polygon-network representations, incorporating geometric constraints into both modeling and inference. Chapter 4 integrates the resulting mobility summaries into applied analysis, demonstrating how time-weighted activity measures can be combined with external spatial information to study contextual exposure in public health settings. Together, these contributions provide a coherent model-based approach to spatio-temporal inference on human mobility that links data generation, estimation, spatial representation, and scientific application within a unified statistical framework.