Advanced non-homogeneous dynamic Bayesian network models for statistical analyses of time series data

Non-homogeneous dynamic Bayesian network models (NH-DBNs) have become popular statistical tools for analyzing time series data in order to infer the relationships between units from the data. We consider
those models where a set of changepoints is employed to divide the data into disjoint segments. The changepoints are time points in which after them the general trend of the data changes. Thereafter, data within each segment are modeled with linear regression model. Some segments might be rather short and including only a few data points. Statistical inference in short segments with just a few (insufficient) data may lead to wrong conclusions. This, indeed, calls for models which make use of information sharing among segments. Recently, models with different coupling mechanisms between segments have been introduced. The main shortcoming of these models are that they cannot deal with time series data in which some parameters are dissimilar (uncoupled) over segments. Another scenario also happens when we encounter some time series data which have been measured under different experimental conditions. In this case we can assume each dataset per se a separate segment. Not rarely only some parameters depend on the condition while the other parameters stay constant across conditions. These situations call for advanced models with an effective mechanisms for coupling and uncoupling simultaneously. In this thesis we introduced four novel models which can deal with the above-mentioned situations and our empirical results have shown that our models lead to improved network reconstruction accuracies and outperform all competing models.