Full disclosure: I have papers using B (on structure learning using BIC, which is an approximation to a posterior of a graphical model), and using F (on estimation of causal effects). I have no horse in this race.

Bayes rule is the answer to that problem that provides the promise of a solution.

See, this is precisely the kind of stuff that makes me shudder, that regularly appears on LW, in an endless stream. While Scott Alexander is busy bible thumping data analysts on his blog, people here say stuff like this.

Bayes rule doesn't provide shit. Bayes rule just says that p(A | B) p(B) = p(B | A) p(A).

Here's what you actually need to make use of info in this study:

(a) Read the study.

(b) See if they are actually making a causal claim.

(c) See if they are using experimental or observational data.

(d) Experimental? Do we believe the setup? Are we in a similar cohort? What about experimental design issues? Observational? Do they know what they are doing, re: causality-from-observational-data? Is their model that permits this airtight (usually it is not, see Scott's post on "adjusting for confounders". Generally to really believe that adjusting for confounders is reasonable you need a case where you know all confounders are recorded by definition of the study, for instance if doctors prescribe medicine based only on recorded info in the patient file).

(e) etc etc etc

I mean what exactly did you expert, a free lunch? Getting causal info and using it is hard.

p.s. If you skeptical about statistics papers that adjust for confounders, you should also be skeptical about missing data papers that assume MAR (missing at random). It is literally the same assumption.