When performing causal inference, endogeneity issues can take form of omitted variables, measurement erros and simultaneity issues and one of them can cause another.

In this case i am specifically interested in simultaneity issues, namely, we are unsure if X → Y or if Y → X or we may even know that both of them occur in our dataset.

Consider e.g the following graphical model:

I heard about an interesting method to deal with this that i want to know more about.

Assume that we are interested in knowing the effect of bi_1 → bi_2

The method works as follows, create two dags(in the case above) where we remove the bidirectionality between bi_1 and bi_2 and instead just keep one of the arrows in the dags, e.g dag_1 may have bi_1 → bi_2 and dag_2 may have bi_2 → bi_1.

We then compute the relative likelihood of the dags and weight the effect of the dag we are interested in with this calculated weight.

I happened to hear about this in school as a measure of attacking simultaneity issues but i cant find any resources what so ever online. Obviously there are vast resources on bayesian networks but googling e.g “simultaneity in bayesian networks” and similar queries render nothing.

I thought this forum(my preferred bayesian modelling framework) might have someone that have experience with these scenarios so i take a shot here:

Does anyone know what this method is called and where i can find more information about it(especially in terms of countering simultaneity issues)?