A Differential Approach to Causality in Staged Trees

In this paper, we apply a recently developed differential approach to inference in staged tree models to causal inference. Staged trees generalise modelling techniques established for Bayesian networks (BN). They have the advantage that they can depict highly nuanced structure impossible to express in a BN and also enable us to perform causal manipulations associated with very general types of interventions on the system. Conveniently, what we call the interpolating polynomial of a staged tree has been found to be an analogue to the essential graph of a BN. By analysing this polynomial in a differential framework, we find that interventions on the model can be expressed as a very simple operation. We can therefore clearly state causal hypotheses which are invariant for all staged trees representing the same causal model. The technology we develop here, illustrated through a simple example, enables us to search for a variety of complex manipulations in large systems accurately and efficiently.