Would it be possible to use bayesian network for regression and/or prediction? I understand that it is a tool one can use to compute probabilities, but I haven't found much material about possible applications for forecasting.
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The Naive Bayes classifier is a type of classifier which is a Bayesian Network (BN). There are also extensions like Tree-Augmented Naive Bayes and more generally Augmented Naive Bayes.
So not only is it possible, but it has been done and there is lots of literature on it.
Most of the applications I see deal with classification rather than regression, but prediction of continuous values is also possible.
A prediction task is essentially a question of "what is $E(Y|X)$" where $Y$ is the variable you want to predict and $X$ is(are) the variable(s) that you observe, so yes you can (and people have) used BNs for it.
Note that a lot of the BN literature for those applications is in the Machine Learning domain.