Let’s suppose that we have two correlated variables (for example mark_in_math and mark_in_physics) but there is no causality between the two variables. For example, the level_of_the_student is a cause for these two variables.
How can we model the Bayesian network containing these two variables (mark in math and mark in physics but not including student_level variable) and of course other variables of the problem while ensuring the correlation between them?
Causatily VS Correlation in Bayesian Network

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Re: Causatily VS Correlation in Bayesian Network
Let the two variables be MM and MP. I would advise having a third variable, called LS and the following structure MM<LS>MP. If you have no data, you will have to estimate the conditional probabilities P(MMLS) and P(MPLS). If you have data for MM and MP, you can learn the parameters without LS being measured using the EM algorithm (standard algorithm used in GeNIe/SMILE).
I hope this helps,
Marek
I hope this helps,
Marek