Graphical models for composable finite Markov processes

Composable Markov processes were introduced by Schweder (1970) in order to capture the idea that a process can be composed of different components where some of these only depend on a subset of the other components. Here we propose a graphical representation of this kind of dependence which has been called 'local dependence'. It is shown that the graph allows to read off further independencies characterizing the underlying Markov process. Also, some standard methods for inference are adapted to exploit the graphical representation, e.g. for testing local independence.