I don’t see how being a Bayesian gets you out of cherry-picking your causal structure from a large set. You still have to decide which variables are conditional on which other variables.
You put in all the variables, use a hierarchical structure for the prior, use a weakly informative hyperprior, and let the data sort itself out if it can. Key phrase: automatic relevance determination; David MacKay originated the term while doing Bayesian inference for neural nets.
I don’t see how being a Bayesian gets you out of cherry-picking your causal structure from a large set. You still have to decide which variables are conditional on which other variables.
You put in all the variables, use a hierarchical structure for the prior, use a weakly informative hyperprior, and let the data sort itself out if it can. Key phrase: automatic relevance determination; David MacKay originated the term while doing Bayesian inference for neural nets.