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I am learning DAGs and Equivalence Class of DAGs, I am reading the material by Prof. Campos Ibáñez here: https://www.cs.cmu.edu/afs/cs/project/jair/pub/volume18/acid03a-html/node2.html

However, I don't understand this:

"It should be noted that each structure in the DAG space is not always different from the others in terms of its representation capability: if we interpret the arcs in a DAG as causal interactions between variables, then each DAG represents a different model; however, if we see a DAG as a set of dependence/independence relationships between variables (that permits us to factorize a joint probability distribution), then different DAGs may represent the same model. Even in the case of using a causal interpretation, if we use observation-only data (as opposed to experimental data where some variables may be manipulated), it is quite common for two Bayesian networks to be empirically indistinguishable."

Could any please explain your understanding about this part? What are the differences between causal interactions and independence/dependence relationship? I'm new and a little bit confused to this.

Your help is really appreciated!

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    $\begingroup$ Note that DAGs are a more general concept than their use in graphical models. Your question is about the modelling, not DAGs per se. (<rant>Why, oh why do MLists seem to have to take over terminology that's older than their field?</rant>) $\endgroup$ – Raphael Sep 4 '17 at 7:40

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