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Graphical Models for Composable Finite Markov Processes

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  • VANESSA DIDELEZ

Abstract

. 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.

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  • Vanessa Didelez, 2007. "Graphical Models for Composable Finite Markov Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(1), pages 169-185, March.
    • Handle: RePEc:bla:scjsta:v:34:y:2007:i:1:p:169-185
    DOI: 10.1111/j.1467-9469.2006.00528.x
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    Cited by:

    1. Jonas Hallgren & Timo Koski, 2016. "Testing for Causality in Continuous Time Bayesian Network Models of High-Frequency Data," Papers 1601.06651, arXiv.org.
    2. Beate Jahn & Sarah Friedrich & Joachim Behnke & Joachim Engel & Ursula Garczarek & Ralf Münnich & Markus Pauly & Adalbert Wilhelm & Olaf Wolkenhauer & Markus Zwick & Uwe Siebert & Tim Friede, 2022. "On the role of data, statistics and decisions in a pandemic," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(3), pages 349-382, September.
    3. Sarah Friedrich & Gerd Antes & Sigrid Behr & Harald Binder & Werner Brannath & Florian Dumpert & Katja Ickstadt & Hans A. Kestler & Johannes Lederer & Heinz Leitgöb & Markus Pauly & Ansgar Steland & A, 2022. "Is there a role for statistics in artificial intelligence?," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(4), pages 823-846, December.
    4. 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.
    5. 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.
    6. 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.
    7. 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.

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