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Abstract:
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Unifying inference perspectives has been a desideratum for (some) statisticians throughout the history. Our recent study of individualized inferences (Liu and Meng, 2016) suggests that this goal is simultaneously far and near. It is far because frequentist and Bayesian, in their respectively most dogmatic forms, are at opposite extremes of the relevance-robustness spectrum. Unconditional frequnentists prefer procedures that have the widest applicability (i.e., robustness) but with little guarantee on the relevance of the resulting inference for any particular problem. Pure subject Bayesians seek to fully individualize each inference to achieve maximal relevance, yet they pay the price of being most vulnerable to the misspecification of a priori assumptions. It is near because the differences among essentially all statistical inferences perspectives are merely a matter of choosing different replications for probabilistic quantification, with the choice determined by how individualized the inference should be, that is, by which relevance-robustness trade-off one is willing to make. We demonstrate these trade-offs for point and set estimations as well as for hypothesis testing.
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