First formulations of graphical Markov models started about 40 years ago, vigorous development is ongoing. These new types of multivariate statistical models combine two simple but most powerful notions: data generating processes in sequences of single and in joint responses and conditional independences captured by graphs. The models build on early work at beginning of the last century by geneticist Sewall Wright and probabilist Andrej Markov.
One primary objective is to uncover graphical representations that lead to an understanding of data generating processes. Such processes are no longer restricted to linear relations but they contain as special cases: linear dependences, subclasses of structural equations for longitudinal studies and models for sequences of interventions. In particular, response variables may be vector variables that contain discrete or continuous components or both types.