Bayesian Approaches to Observability and Extensions of Copula State Space Models and their Applications

In many scientific fields, understanding complex dependence structures in
multivariate time series is essential for making reliable inferences and
predictions. Classical state space models, while widely used, often rely on
restrictive assumptions that limit their ability to capture nonlinear and
non-Gaussian dynamics. This thesis advances the framework of copula state space
models, providing a flexible approach to modeling dependencies in both latent states
and observations.

New theoretical foundations are established by introducing a novel framework for
assessing observability, allowing researchers to determine whether latent states and
model parameters can be uniquely recovered from data. Furthermore, copula state
space models are extended to include multivariate latent states and
covariate-dependent dependence structures, increasing their flexibility and
practical relevance. Inference for the proposed models is carried out within a
Bayesian framework.

The developed methods are demonstrated through real-world applications, including
air pollution data and mortality statistics. The results show how flexible
dependence modeling can reveal hidden dynamics, improve model performance, and
uncover structural changes, such as shifts in dependence patterns during the
COVID-19 pandemic.

• By (author) Ariane T. Hanebeck