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Graphical models for marked point processes based on local independence

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  • Vanessa Didelez

Abstract

Summary. A new class of graphical models capturing the dependence structure of events that occur in time is proposed. The graphs represent so‐called local independences, 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 the corresponding local independence graphs differ considerably from classical graphical models. Hence a new notion of graph separation, which is 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 dependences as well as computational simplifications are discussed.

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  • Vanessa Didelez, 2008. "Graphical models for marked point processes based on local independence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 245-264, February.
    • Handle: RePEc:bla:jorssb:v:70:y:2008:i:1:p:245-264
    DOI: 10.1111/j.1467-9868.2007.00634.x
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    2. Mohammad Masoud Rahimi & Elham Naghizade & Mark Stevenson & Stephan Winter, 2023. "SentiHawkes: a sentiment-aware Hawkes point process to model service quality of public transport using Twitter data," Public Transport, Springer, vol. 15(2), pages 343-376, June.
    3. Tata Subba Rao & Granville Tunnicliffe Wilson & Michael Eichler & Rainer Dahlhaus & Johannes Dueck, 2017. "Graphical Modeling for Multivariate Hawkes Processes with Nonparametric Link Functions," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(2), pages 225-242, March.
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    5. Jan M. Hoem & Lesia Nedoluzhko, 2008. "Marriage formation as a process intermediary between migration and childbearing," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 18(21), pages 611-628.
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    7. Eichler, M. & Didelez, V., 2009. "On Granger-causality and the effect of interventions in time series," Research Memorandum 003, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    8. Jan M. Hoem & Lesia Nedoluzhko, 2008. "Marriage formation as a process intermediary between migration and childbearing," MPIDR Working Papers WP-2008-015, Max Planck Institute for Demographic Research, Rostock, Germany.
    9. Daniel Commenges & Anne Gégout‐Petit, 2009. "A general dynamical statistical model with causal interpretation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 719-736, June.
    10. Ørnulf Borgan & Håkon K. Gjessing, 2019. "Special issue dedicated to Odd O. Aalen," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(4), pages 587-592, October.
    11. Oisín Ryan & Ellen L. Hamaker, 2022. "Time to Intervene: A Continuous-Time Approach to Network Analysis and Centrality," Psychometrika, Springer;The Psychometric Society, vol. 87(1), pages 214-252, March.
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