Thanks for the question. It may be better to do a unified analysis with all 50 candidate SNPs. But if you do separate analyses you are always assuming in effect that the 50 priors are independent.
But to your point, there are two issues going on:
- multiplicity such as discussed at the top of this topic, which does not really apply to Bayes since you can have evidence about each SNP standing on its own
- getting the model right and being properly skeptical
On the second bullet, “getting the model right” might mean getting the “population” of SNP effects to be what we expect from biology. If you think this “population” is sparse, e.g., you think there is a small number of SNPs with decent sized effects, then you would specify in the Bayesian model a shrinkage prior like the horseshoe prior and analyze all 50 jointly.
If you did separate analyses I suppose you could have a N(0, 0.1) prior for each SNP’s log odds ratio.