Dynamic graphical models using shrinkage process priors

Abstract

This overarching thesis presents innovative methodologies for estimating high dimensional time series data using graphical models. The content is divided into two main chapters, which are structured in the form of articles, supplemented by introductory and concluding chapters. The first article introduces the Dynamic Graphical Variable Selection model, which combines dynamic linear models with spike-and-slab priors for variable selection, allowing for the inference of connectivity in brain regions with varying weights and graphical structures over time. Demonstrating computational efficiency and competitiveness against prior methodologies in handling high-dimensional data, the model is illustrated through numerical experiments. The proposal is particularly appealing for research contributions, especially aimed at brain/cortical mapping related to cognitive issues. Similarly, the second article introduces the Dynamic Graphical Variable Selection for Directed Acyclic Graph model, employing a Dynamic Horseshoe Process for variable selection and incorporating an algorithm to search for directed acyclic graph structures. This approach demonstrates superior performance and increased flexibility in estimating networks for groups of individuals over time, as evidenced by simulated and real data experiments. The results suggest that our estimates outperform previous network search methodologies and demonstrate greater flexibility. Together, these articles contribute significant advancements to the understanding of brain connectivity dynamics, providing promising avenues for future research in neuroscience.