How can we combine learnings from multiple experiments in a single causal model?

Question

I would like to use a causal network modelling to model the interaction of several variables and the effects of interventions. I have measurements for all priors of the model, that is without any interventions, and a well defined structure as DAG. Also, assume there are no hidden variables.

We have the possibility to run experiments and measure the causal effects of interventions on specific variables. Assume we can set one variable per experiment. That is we have measurements of the type $P(A / do(B) )$ using Pearls’ notation. Different experiments lead to different and new learnings and measurements of the type $P(A / do(C) )$.

Is there a framework on how to combine these learnings from many different experiments in order to infer quantities such as $P(A / do(B), do(C) )$ without running an experiment that sets both $B$ and $C$?

Answer 1

Without context this is hard to say --- I will point you to the relevant literature so you can get started. It seems that what you want to do is related to the data fusion problem --- how to combine data of different settings and interventions. You can read the papers by Elias Barenboin, specially this one with Pearl.