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I am new to stats. I am reading the book: Bayesian Networks With Examples in R and already in the first pages, some claims are made which I don't follow.

The author says:

Age and Sex are not influenced by any of the other variables. Therefore, there are no arcs pointing to either variable. On the other hand, both Age and Sex have a direct influence on Education. It is well known, for instance, that the number of people attending universities has increased over the years. As a consequence, younger people are more likely to have a university degree than older people.

His statement doesn't seem to make sense to me... I see it as 'both ways', age depends on education, and education depends on age... Yes, he is right saying that age influences education, if the person is 20 years old is likely to be at undergrad level, but the same goes the other way around if the person has a postdoc, is likely to be > 29 years old...

My question is, is this just a dummy example, with no importance,or am I missing some important theory/aspect?

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You're correct, when one is given the other can be inferred. This is always the case if the variables are dependent. But, the discussion in the text is about causality. Bayesian networks encode causal relationships. So, the direction of the arrows is the flow of causality in the model. Otherwise, you'd have always arrows in both directions. The word influence in the text tries to emphasise this concept, however I think the example could have been better.

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  • $\begingroup$ Well, I agree with you, but the author is just saying the opposite, he says: "causal, is difficult to justify in most situations; for this reason, in general we speak about dependence relationships instead of causal effects". $\endgroup$
    – Chicago1988
    Commented Dec 25, 2019 at 16:25
  • $\begingroup$ He is saying that "causality is difficult to justify". This comment is abut semantics, not that causality in some even mild sense is not being present there. $\endgroup$
    – gunes
    Commented Jan 21, 2020 at 13:11

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