Bayesian hierarchical modeling of array-structured demographic data

Reliable inference for complex demographic phenomena is essential for understanding population health dynamics and informing public policies. The relevance of this endeavor has stimulated increasing interest in rigorous statistical models for high-dimensional demographic data with complex dependence structures. Recent research has provided valuable insights and effective predictive strategies, but often focuses on specific dimensions at the expense of others. This perspective rules out the possibility to infer more nuanced, yet fundamental, demographic patterns that span across multiple dimensions (e.g., calendar years, age classes, causes of death, countries). We contribute to this line of research by developing novel hierarchical Bayesian procedures for joint modeling of cross-sectional and temporal interactions in array-structured demographic data. This thesis addresses, in particular, three main objectives through state-of-the-art methodologies accounting for demographic processes' core characteristics, while incorporating dynamic partitioning mechanisms. First, we propose a flexible model for age-period log-mortality rates inducing local clusters of countries. To address the functional nature of the age component, we employ b-spline expansions with dynamic coefficients. Local clustering of the log-mortality rates is achieved through a dependent random partition model on the coefficients that allows grouping structures to vary flexibly across different combinations of ages and periods. We unveil unexplored relationships between countries, opening new directions for demographic research. Second, we extend stochastic block models to analyze sequences of directed networks encoding co-occurrences of underlying and contributing causes of death. We handle categorically weighted edges assuming block-specific Categorical-Dirichlet distributions, implement a double partition framework to account for asymmetric relationships between underlying and contributing causes, and describe the node clusters through dependent random partitions to ensure smooth evolution of block structures across age classes. Application to 2019 US data reveals cause partitioning that moves beyond traditional medical classifications into more nuanced groupings. Third, we develop a methodology for dynamic clustering of countries based on their age-specific leading cause of death sequences over time. We model each country's sequence as a categorical trajectory and handle their grouping through a mixture model with exponential-distance components based on Hamming distances, which enables characterization of clusters through a modal sequence and scale parameters describing the heterogeneity of each age-group. The induced partition is allowed to evolve smoothly across years through a temporal random partition model, enabling the identification of clustering structures in leading mortality causes which renovate standard epidemiological transition theories.