Multiplicity comes from the chances (over study repetitions and data looks) you give data to be more extreme (if the null hypothesis holds), not from the chances you give an effect to be real. It is only the latter that is of concern to a Bayesian. Bayesians entertain only one dataset at a time, and if one computes posterior probabilities of efficacy multiple times, it is only the last value calculated that matters. — Continuous Learning from Data: No Multiplicities from Computing and Using Bayesian Posterior Probabilities as Often as Desired