Advanced Bayesian regression and dynamic network modelling

The focus of this PhD thesis has been on two well-known and widely applied statistical model classes, namely, the class of dynamic Bayesian network (DBN) models and the class of seemingly unrelated regression (SUR) models. For both model classes we have proposed methodological improvements and we have shown that the improvements can yield significantly better results.
Dynamic Bayesian networks (DBNs) are popular tools for learning the dependencies among random variables that have been measured over time. Like for discrete dynamical systems, the key assumption for DBN models is that all regulatory interactions are subject to a time lag of one time unit. Another popular assumption is that the task of learning the network structure can be decomposed into independent regression tasks. In computational systems biology, DBN models are used to reconstruct the structures of cellular networks such as gene regulatory networks and protein signalling pathways. The class of non-homogeneous DBN (NH-DBN) models allows for modelling regulatory processes that are subject to temporal changes. This is done by subdividing a long time series into disjoint segments with segment-specific interaction parameters. To avoid model-over-flexibility it has been proposed to couple the segment-specific parameters such that they are encouraged to stay similar among segments. In this PhD thesis we have proposed various model refinements for the globally coupled NH-DBN model by Grzegorczyk and Husmeier (2013) cf. Chapters 3-5.
Seemingly unrelated regression (SUR) models are another popular statistical tool. In SUR models it is assumed that there is a set of regression problems and that those models have correlated errors. Because of the correlated errors, the regression problems are dependent (`related') and cannot be inferred independently. In this PhD thesis, we have developed a new sparse SUR (SSUR) model; cf. Chapter~2.