Structure and Heterogeneity Learning in Dynamical Bayesian Networks

Public health and socio-economic systems exhibit complex interdependencies, regional heterogeneity, and severe data limitations. Indicators spanning deprivation, economic activity and health outcomes are typically observed at low temporal resolution and affected by noise and sparseness, making their dependency networks difficult to identify when structure is unknown or only partly informed by expert knowledge. This thesis develops likelihood-based Bayesian network and state-space methods for learning these structures. Bayesian Belief Networks first validate and refine elicited system maps using cross-sectional data from English and Scottish Local Authorities. Dynamical Bayesian Networks are then formulated as linear Gaussian state-space models, with network structure encoded through adjacency constraints.

The principal methodological contribution is a doubly iterative Expectation–Maximisation algorithm enabling joint maximum-likelihood estimation of network structure and model parameters for structured Dynamical Bayesian Networks under short time-series constraints, exploiting cross-sectional replication across multiple subsystems. In simulation, this approach achieves full recovery of true network structures for small systems and 60–80% structural agreement with the ground truth for larger systems; on real Scottish data, a K-fold-selected network achieves a 27% improvement in validation score over the expert-informed network.

To capture regional heterogeneity, the thesis extends linear Gaussian state-space models with mixed-effects and mixture structures, jointly learned within a unified Expectation-Maximisation estimation framework. In simulation, the resulting latent-state mixed-effects formulation reduces normalised mean-squared parameter estimation error by approximately 32% relative to a simpler balancing estimator and 25% relative to a constrained Lagrange-multiplier alternative. These results demonstrate recovery of meaningful network dependencies, identification of regional disparities, and interpretable insights relevant to public health policy. Overall, the thesis contributes new methodological tools for network structure learning and demonstrates their practical value for modelling complex public health and socio-economic systems under realistic data limitations.