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Jointly interventional and observational data: estimation of interventional Markov equivalence classes of directed acyclic graphs

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  • Alain Hauser
  • Peter Bühlmann

Abstract

type="main" xml:id="rssb12071-abs-0001"> In many applications we have both observational and (randomized) interventional data. We propose a Gaussian likelihood framework for joint modelling of such different data types, based on global parameters consisting of a directed acyclic graph and corresponding edge weights and error variances. Thanks to the global nature of the parameters, maximum likelihood estimation is reasonable with only one or few data points per intervention. We prove consistency of the Bayesian information criterion for estimating the interventional Markov equivalence class of directed acyclic graphs which is smaller than the observational analogue owing to increased partial identifiability from interventional data. Such an improvement in identifiability has immediate implications for tighter bounds for inferring causal effects. Besides methodology and theoretical derivations, we present empirical results from real and simulated data.

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  • Alain Hauser & Peter Bühlmann, 2015. "Jointly interventional and observational data: estimation of interventional Markov equivalence classes of directed acyclic graphs," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(1), pages 291-318, January.
    • Handle: RePEc:bla:jorssb:v:77:y:2015:i:1:p:291-318
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    File URL: http://hdl.handle.net/10.1111/rssb.2014.77.issue-1
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    Cited by:

    1. Castelletti, Federico & Peluso, Stefano, 2021. "Equivalence class selection of categorical graphical models," Computational Statistics & Data Analysis, Elsevier, vol. 164(C).
    2. Federico Castelletti & Guido Consonni, 2020. "Discovering causal structures in Bayesian Gaussian directed acyclic graph models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(4), pages 1727-1745, October.
    3. Federico Castelletti & Guido Consonni & Luca Rocca, 2022. "Discussion to: Bayesian graphical models for modern biological applications by Y. Ni, V. Baladandayuthapani, M. Vannucci and F.C. Stingo," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(2), pages 261-267, June.
    4. Jonas Peters & Peter Bühlmann & Nicolai Meinshausen, 2016. "Causal inference by using invariant prediction: identification and confidence intervals," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(5), pages 947-1012, November.
    5. Christian Gische & Manuel C. Voelkle, 2022. "Beyond the Mean: A Flexible Framework for Studying Causal Effects Using Linear Models," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 868-901, September.
    6. Federico Castelletti & Guido Consonni, 2021. "Bayesian inference of causal effects from observational data in Gaussian graphical models," Biometrics, The International Biometric Society, vol. 77(1), pages 136-149, March.

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