No, the uncertainty here isn't about which of the two studies a datapoint came from, but about whether (for a specific treatment/intervention) the correlational study datapoint was drawn from the same distribution as the randomized study datapoint or a different one, and (over all treatments/interventions) what the probability of being drawn from the same distribution is. Maybe it'll be a little clearer if I narrate how the model might go. So say you start off with a prior probability of 50-50 about which group a result is drawn from, a switching probability that will be tweaked as you look at data. (If you are studying turtles which could be from a large or a small species, then if you find 2 larger turtles and 8 smaller, you're probably going to update from P=0.5 to a mixture probability more like P>0.20, since it's most likely - but not certain - that 1 or 2 of the larger turtles came from the large species and the 8 smaller ones came from the small species.) For your first datapoint, you have a pair of results: xyzcillin reduces all-cause mortality to RR=0.5 from a correlational study (cohort, cross-sectional, case-control, whatever), and the randomized study of xyzcillin has RR=1.1. What does this mean? Now, of course you know that 0.5 is the correlational result and 1.1 is the randomized result, but we can imagine two relatively distinct scenarios here: 'xyzcillin actually works but the causal effect is really more like RR=0.7 and the randomized trial was underpowered', or, 'xyzcillin has no causal effect whatsoever on mortality and it's just a bunch of powerful confounds producing results like RR=0.6-0.8'. We observe that 1.1 supports the latter more, and we update towards 'xyzcillin has 0 effect' and now give 'non-causal scenarios are 55% likely', but not too much because the xyzcillin studies were small and underpowered and so they don't support the latter scenario that much. Then for the next datapoint, 'abcmycin reduces lung cancer', we get a pair look