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A0593
Title: Familial inference Authors:  Ryan Thompson - Monash University (Australia) [presenting]
Catherine Forbes - Monash University (Australia)
Steven MacEachern - The Ohio State University (United States)
Mario Peruggia - The Ohio State University (United States)
Abstract: Statistical hypotheses are translations of scientific hypotheses into statements about one or more distributions, often concerning their center. Tests that assess statistical hypotheses of center implicitly assume a specific center, e.g., the mean or median. Yet, scientific hypotheses do not always specify a particular center. This ambiguity leaves the possibility of a gap between scientific theory and statistical practice that can lead to rejection of a true null. In the face of replicability crises in many scientific disciplines, ``significant results'' of this kind are concerning. Rather than testing a single center, we propose testing a family of plausible center'', such as that induced by the Huber loss function (the ``Huber family"). Each center in the family generates a testing problem, and the resulting family of hypotheses constitutes a familial hypothesis. A Bayesian nonparametric procedure is devised to test familial hypotheses, enabled by a novel pathwise optimization routine to fit the Huber family. We verify the favorable properties of the new test through numerical simulation in one- and two-sample settings. Two experiments from psychology serve as real-world case studies.