A new class of graphical models capturing the dependence structure of events that occur in time is proposed. The graphs represent so-called local independencies, meaning that the intensities of certain types of events are independent of some (but not necessarilly all) events in the past. This dynamic concept of independence is asymmetric, similar to Granger non-causality, so that the corresponding local independence graphs differ considerably from classical graphical models. Hence a new notion of graph separation, called δ-separation, is introduced and implications for the underlying model as well as for likelihood inference are explored. Benefits regarding facilitation of reasoning about and understanding of dynamic dependencies as well as computational simplifications are discussed.
In more general cases, a class of graphical models of marked point processes is proposed in REF to capture the local independence over various marks.
Graphical models for marked point processes based on local independence
arXiv: Statistics Theory
Mathematics Computer Science