Extensions of graphical models with applications in genetics and genomics

The living cell is a complex system of interacting molecules, in which genes are transcribed into RNAs and translated into proteins. Most biological characteristics arise from complex interactions between the cell's numerous components. Therefore, a key challenge for biology is to understand the structure and the dynamics of the complex inter- and intra-cellular web of interactions that contribute to the structure and function of a living cell.

The behavior of most complex systems, from the cell to the Internet, emerges from the activity of many components that pairwise interact with each other. At an abstract level, these components can be shown as a series of nodes that are connected to each other by links, where each link shows the interaction between two components. The nodes and links together form a network or, in more formal language, a graph.

The objectives of this work have been to extend graphical models for different data structures and to enlarge the applicability of graphical models in various fields, particularly in systems genetics. In this thesis, we have developed a method based on undirected graphical models to infer direct relationships between components of a system. In addition, we have extended graphical models to high-dimensional time-series data with non-Gaussian structure, where we combined directed and undirected graphical models to explore dynamic and contemporaneous interactions. We have implemented the proposed methods as user-friendly software called netgwas, and tsnetwork which is freely accessible for users.