  Replication studies are increasingly conducted but there is no established
statistical criterion for replication success. We propose a novel approach
combining reverse-Bayes analysis with Bayesian hypothesis testing: a sceptical
prior is determined for the effect size such that the original finding is no
longer convincing in terms of a Bayes factor. This prior is then contrasted to
an advocacy prior (the reference posterior of the effect size based on the
original study), and replication success is declared if the replication data
favour the advocacy over the sceptical prior at a higher level than the
original data favoured the sceptical prior over the null hypothesis. The
sceptical Bayes factor is the highest level where replication success can be
declared. A comparison to existing methods reveals that the sceptical Bayes
factor combines several notions of replicability: it ensures that both studies
show sufficient evidence against the null and penalises incompatibility of
their effect estimates. Analysis of asymptotic properties and error rates, as
well as case studies from the Social Sciences Replication Project show the
advantages of the method for the assessment of replicability.
