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The Bayesian Networks and Logistic regression can be used to predict events or give to each customer the propensity to have a behavior.

Which are the advantages or disadvantages of these 2 methods? When is better use the first and when is better use the other?

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A Bayesian network is a graphical representation of an arbitrary probabilistic model. Logistic regression is one very specific kind of probabilistic model, and it can be represented by a Bayesian network. So you can't really say that one is better than another at prediction.

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