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I just created a Bayesian correlation matrix and I was wondering if the reported Bayes factors take into account multiple comparisons somehow.
No, they don't (you can check by eliminating some correlations -- the BF between that remains should not change). We could actually implement a correction, as we did for our post-hoc test for ANOVA. I'll take this up with the team. See also https://psyarxiv.com/s56mk for a discussion on Bayesian methods for multiple comparison corrections.