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

Ariane T. Hanebeck

ISBN 978-3-8325-6064-5
196 Seiten, Erscheinungsjahr: 2026
Preis: 41.00 €

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.