  Chain event graphs are a family of probabilistic graphical models that
generalise Bayesian networks and have been successfully applied to a wide range
of domains. Unlike Bayesian networks, these models can encode context-specific
conditional independencies as well as asymmetric developments within the
evolution of a process. More recently, new model classes belonging to the chain
event graph family have been developed for modelling time-to-event data to
study the temporal dynamics of a process. However, existing model selection
algorithms for chain event graphs and its variants rely on all parameters
having conjugate priors. This is unrealistic for many real-world applications.
In this paper, we propose a mixture modelling approach to model selection in
chain event graphs that does not rely on conjugacy. Moreover, we also show that
this methodology is more amenable to being robustly scaled than the existing
model selection algorithms used for this family. We demonstrate our techniques
on simulated datasets.
