Computational methods for k-parametric dynamic generalized linear models

Abstract

This dissertation presents a series of interconnected studies aimed at advancing the field of Bayesian time series analysis through the development and application of Generalized Dynamic Linear Models (DGLM). By focusing on sequential information updating within the exponential family for both univariate and multivariate responses, this work provides novel methodologies that enhance real-time analysis, monitoring, and decision-making capabilities across various domains. The research begins with the introduction of a new method for sequential updating in DGLMs, emphasizing computational efficiency and the ability to generate timely forecasts. Subsequent studies extend the initial methodology to accommodate a wider range of distributions within the exponential family and explore its application to multiple time series data, incorporating mixed effects to model interdependencies. The dissertation addresses both the theoretical underpinnings and practical implications of these methods, demonstrating their effectiveness through simulated and real-world data applications. Finally, the ongoing development of the kDGLM R package is discussed, highlighting its role in the broader context of Bayesian time series analysis and its potential for future enhancements. The dissertation not only contributes to the academic discourse but also provides practical tools and methods that can be readily employed in various fields, showcasing the symbiotic relationship between theoretical innovation and practical application in statistical science.