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Schwaferts, Patrick; Augustin, Thomas (17. November 2020): Bayesian Decisions using Regions of Practical Equivalence (ROPE): Foundations. Department of Statistics: Technical Reports, No.235


Kruschke [2018] proposes the so called HDI+ROPE decision rule about accepting or rejecting a parameter null value for practical purposes using a region of practical equivalence (ROPE) around the null value and the posterior highest density interval (HDI) in the context of Bayesian statistics. Further, he mentions the so called ROPE-only decision rule within his supplementary material, which is based on ROPE, but uses the full posterior information instead of the HDI. Of course, if it is about formalizing and guiding decisions then statistical decision theory is the framework to rely on, and this technical report elaborates the decision theoretic foundations of both decision rules. It appears that the foundation of the HDI+ROPE decision rule is rather artificial compared to the foundation of the ROPE-only decision rule, such that latter might be characterized as being closer to the underlying practical purpose than former. Still, the ROPE-only decision rule employs a truly arbitrary, and thus debatable, choice of loss values.