Bayesian model determination in complex systems

One of the main challenges in modern science is the accurate and complete description of complex systems. The difficulty of modeling complex systems lies partly in their topology and how they form rather complex networks. From this perspective, our interest to modeling networks is part of a broader movement towards research on complex systems.

In this thesis, we develop several statistical methods that jointly model the underlying network and its structure among variables in the system. These methods are easy to implement and computationally feasible for complex networks. We cover the theory and computational details of the methods. We have extended our statistical method such that it works for different types of complex data. We applied it to a Dupuytren disease dataset to discover potential risk factors. We have implemented our methods as a user-friendly statistical software called BDgraph, which is freely available online.