Say I have written down a directed acyclic graph (a causal model) with a few dozen variables. Moreover, I have a dataset with observations for many (though not all) of the variables. For simplicity, let us assume that all variables are categorical. Which methods are state of the art for identifying the model parameters / the posteriors in the graph?
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$\begingroup$ Perhaps you can tell us which methods (e.g., G-estimation, etc.) you consider familiar, but not state of the art? $\endgroup$– AlexisCommented Dec 14, 2021 at 16:58
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$\begingroup$ @Alexis to be honest, I am not yet really familiar with any method and am trying to select the best approach to start with in a new project. My current best guess would be to simply use some MCMC variant, but as the number of variables is in the dozens (observations in the hundred thousands) I am unsure whether that's actually feasible. I don't really know which alternative methods would be suitable. Maybe EM+message passing? $\endgroup$– Eike P.Commented Dec 15, 2021 at 13:25
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$\begingroup$ MCMC is a method of estimation, I do not think of MCMC as a causal calculus. Have you read any books of causal estimation yet? $\endgroup$– AlexisCommented Dec 15, 2021 at 18:27
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$\begingroup$ @Alexis Yes, although probably not as many and as deeply as I should have. I am a bit confused by your comment; the method of estimation is exactly what I am interested in? MCMC can be used for inferring causal effects in causal models, cf., e.g., Koller's/Friedman's book on probabilistic graphical models or this paper. $\endgroup$– Eike P.Commented Dec 16, 2021 at 10:18
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$\begingroup$ Maybe read Pearl's The Book of Why, followed by his Causality? MCMC is a statistical estimation technique (or group of techniques), but that does not mean all statistical estimates made with MCMC are causal estimates. $\endgroup$– AlexisCommented Dec 16, 2021 at 19:09
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