Odd—I always felt like d-separation was the same thing on causal diagrams and on Bayes networks. Although, I also understood Bayes network as being a model of the causal directions in a situation, so perhaps that’s why.
Manfred’s excellent example needs equally excellent counterparts for other possibilities.
Sorry for not being clear. The d-separation criterion is the same in both Bayesian networks and causal diagrams, but its meaning is not the same. This is because an arrow A → B in a causal diagram means (loosely) that A is a direct cause of B at the level of granularity of the model, while an arrow A → B in a Bayesian network has a more complicated to explain meaning having to do with the Markov factorization and conditional independence. D-separation talks about arrows in both cases, but asserts different things due to a difference in the meaning of those arrows.
A Bayesian network model is just a statistical model (a set of joint distributions) associated with a directed acyclic graph. Specifically it’s all distributions p(x1, …, xk) that factorize as a product of terms of the form p(x_i | parents(x_i)). Nothing more, nothing less. Nothing about causality in that definition.
I think examples for (1),(2),(3) are simpler than Manfred’s Berkson’s bias example.
(1) A ← C → B
Most clearly non-causal associations go here: “shoe size correlates with IQ” and its kin.
(2) A → C → B, and
(3) A ← C ← B
Classic scientific triumphs go here: “smoking causes cancer.” Of note here is that if we can find an observable unconfounded C that intercepts all/most of the causal pathway, this is extremely valuable for estimating effects. If you can design an experiment with such a C, you don’t even have to randomize A.
Odd—I always felt like d-separation was the same thing on causal diagrams and on Bayes networks. Although, I also understood Bayes network as being a model of the causal directions in a situation, so perhaps that’s why.
Manfred’s excellent example needs equally excellent counterparts for other possibilities.
Sorry for not being clear. The d-separation criterion is the same in both Bayesian networks and causal diagrams, but its meaning is not the same. This is because an arrow A → B in a causal diagram means (loosely) that A is a direct cause of B at the level of granularity of the model, while an arrow A → B in a Bayesian network has a more complicated to explain meaning having to do with the Markov factorization and conditional independence. D-separation talks about arrows in both cases, but asserts different things due to a difference in the meaning of those arrows.
A Bayesian network model is just a statistical model (a set of joint distributions) associated with a directed acyclic graph. Specifically it’s all distributions p(x1, …, xk) that factorize as a product of terms of the form p(x_i | parents(x_i)). Nothing more, nothing less. Nothing about causality in that definition.
I think examples for (1),(2),(3) are simpler than Manfred’s Berkson’s bias example.
(1) A ← C → B
Most clearly non-causal associations go here: “shoe size correlates with IQ” and its kin.
(2) A → C → B, and (3) A ← C ← B
Classic scientific triumphs go here: “smoking causes cancer.” Of note here is that if we can find an observable unconfounded C that intercepts all/most of the causal pathway, this is extremely valuable for estimating effects. If you can design an experiment with such a C, you don’t even have to randomize A.