Chain Event Graphs (CEGs) are a family of graphical statistical models derived from well-known probability trees. They form a generalisation of Bayesian Networks, providing an explicit representation of context-specific conditional dependencies within their topology. During the talk, I will demonstrate on a real cohort study how CEGs enable us to depict various hypotheses about the data generation mechanisms. I will also present how CEGs can be used for statistical inference with an incomplete data set, identifying if the data are missing at random and extracting further conclusions from the patterns of missingness. Finally, I will discuss the problem of data discretisation and present a new method for supervised discretisation without leaving the framework of tree-based models. The method builds on top of the model selection mechanisms for CEGs and does not deteriorate the parsimony of a model, contrary to many existing supervised methods. I will finish off the talk by discussing the potential problems arising when greedy algorithms are used for model selection.