G Freeman and JQ Smith
Dynamic staged trees for discrete multivariate time series: forecasting, model selection and causal analysis
Abstract: A new tree-based graphical model — the dynamic staged tree — is used to model discrete-valued discrete-time multivariate processes which are hypothesised to exhibit certain symmetries concerning how situations might unfold. We define and implement a one-step-ahead prediction algorithm using multi-process modelling and the power steady model. This is robust to short-term variations in the data yet sensitive to underlying system changes. We demonstrate that the whole analysis can be performed in a conjugate way so that the vast model space can be traversed quickly and results communicated transparently. We also demonstrate how to analyse causal hypotheses on this model class. Our techniques are illustrated using a simple educational example.
Keywords: Staged trees, Bayesian model selection, Bayes factors, forecasting, discrete time series, causal inference, power steady model, multi-process model