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Graphical Models for Marked Point Processes based on Local Independence

by Vanessa Didelez

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 necessarily 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.

Keywords: Event history analysis; Conditional independence; Counting processes; Grangercausality; Graphoid; Multistate models.

Full text of the paper (pdf), which has recently appeared in the Journal of the Royal Statistical Society (B).