So, we could add a node to the graph for every single node
That assumes we’re doing graphs and networks.
My problems in this subthread really started when the causal model was defined as “a set of joint distributions defined over potential outcome random variables”—notice how nothing like networks or interventions is mentioned here—and I got curious why a plain-vanilla Bayesian model which also produces a set of joint distributions doesn’t qualify.
Sorry this is a response to an old comment, but this is an easy to clarify question.
A potential outcome Y(a) is a random variable under an intervention, e.g. Y under do(a). It’s just a different notation from a different branch of statistics.
We may or may not choose to use graphs to represent causality (or indeed probability). Some people like graphs, others do not. Graphs do not add anything, they are just a visual representation.
That assumes we’re doing graphs and networks.
My problems in this subthread really started when the causal model was defined as “a set of joint distributions defined over potential outcome random variables”—notice how nothing like networks or interventions is mentioned here—and I got curious why a plain-vanilla Bayesian model which also produces a set of joint distributions doesn’t qualify.
It probably just was a bad definition.
Sorry this is a response to an old comment, but this is an easy to clarify question.
A potential outcome Y(a) is a random variable under an intervention, e.g. Y under do(a). It’s just a different notation from a different branch of statistics.
We may or may not choose to use graphs to represent causality (or indeed probability). Some people like graphs, others do not. Graphs do not add anything, they are just a visual representation.