### On Structural Equations versus Causal Bayes Networks

**We received the following query from Jim Grace, (USGS – National Wetlands Research Center) :**

Hi Judea,

In your 2009 edition of Causality on pages 26-27 you explain your reasoning for now preferring to express causal rules from a Laplacian quasi-deterministic perspective rather than stay with the stochastic conceptualization associated with Bayesian Networks. It seems to me that a practical matter here is the reliance of traditional graph theory on discrete mathematics and the constraints that places on functional forms and, therefore, counterfactual arguments. Despite that clear logic, one sees the occasional discussion of “causal Bayes nets” and I wondered if you would dissuade people (if people can be dissuaded) from trying to evolve a causal modeling methodology with discrete Bayes nets as their starting point?

**Judea Pearl answers:**

Dear Jim,

I would not dissuade people from using either causal Bayesian causal networks or structural equation models, because the difference between the two is so minute that it is not worth the dissuasion. The question is only what question you ask yourself when you construct the diagram. If you feel more comfortable asking: What factors determine the value of this variable” then you construct a structural equation model. If on the other hand you prefer to ask: “If I intervene and wiggle this variable, would the probability of the other variable change?” then the outcome would be a causal Bayes network. Rarely do they differ (but see example on page 35 of Causality).

Thanks for this comment and answer,

My experience is largely with expert-elicited and expert-informed networks, often in cases where the output is not directly observable.

I have asked lots of people what criteria I should use to decide whether a BN or an SEM is appropriate. One common answer is that BNs incorporate uncertainty, so are more likely to be useful with small samples of experts. Do you agree with this assessment?

Comment by Jegar Pitchforth — September 24, 2013 @ 6:55 pm

Dear Judea,

Is there a paper or book that explains succinctly how Bayesian Networks and Structural Equations are related? This would be useful, so that people who use either can relate to models of the other kind.

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Comment by furtdsolinopv — February 21, 2015 @ 10:29 am

Is there a paper or book that explains succinctly how Bayesian Networks and Structural Equations are related? This would be useful, so that people who use either can relate to models of the other kind.

Comment by d — September 3, 2017 @ 10:59 am