Abstract
This tutorial provides an overview of guarantees on the probability of good selection (PGS), i.e., statistical guarantees on selecting - with high probability - an alternative whose expected performance is within a given tolerance of the best. We discuss why PGS guarantees are superior to more popular, related guarantees on the probability of correct selection (PCS) under the indifference-zone formulation. We review existing procedures that deliver PGS guarantees and assess several direct and indirect methods of proof. We compare the frequentist and Bayesian interpretations of PGS and highlight the differences in how procedures are designed to deliver PGS guarantees under the two frameworks.
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