Bayesian Design of “Successful” Replications

Replication of experiments is commonin applied research. However, systematic studies of the goals and motivations of a “replication” are rare. As a consequence, there does not seem to be a precise notion of what a “success” when replicating means. This article discusses some of the possible goals for replication; this leads to different (but precise) notions of “success” when replicating. Bayesian hierarchical models allow for a flexible and explicit incorporation of the assumed relationship among the experiments. Bayesian predictive distributions are a natural tool to compute the probability of the replication being successful, and hence to design the replication so that the probability of success is high enough. Derivations are exemplified with data coming from a noncentral t distribution.