I'm just wondering if Bayesian statistics would be applied consequently from the first study to the last if this makes a meta-analysis obsolete.
For example, let's assume 20 studies which have been done at different timepoints. The estimate or distribution of the first study was done with a uninformative prior. The second study uses the posterior distribution as the prior. The new posterior distribution is now used as prior for the third study and so on.
At the end we have an estimate which contains all the estimates or data which have been done before. Does it makes sense to do a meta-analysis?
Interestingly, I suppose that changing the order of this analysis would also change the last posterior distribution, respectivly, estimate.