Familial inference: tests for hypotheses on a family of centres

Ryan Thompson, Catherine S. Forbes, Steven N. Maceachern, Mario Peruggia

Research output: Contribution to journalArticleResearchpeer-review

Abstract

Statistical hypotheses are translations of scientific hypotheses into statements about one or more distributions, often concerning their centre. Tests that assess statistical hypotheses of centre implicitly assume a specific centre, e.g., the mean or median. Yet, scientific hypotheses do not always specify a particular centre. This ambiguity leaves the possibility for 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 centre, this paper proposes testing a family of plausible centres, such as that induced by the Huber loss function. Each centre 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. The favourable properties of the new test are demonstrated theoretically and experimentally. Two examples from psychology serve as real-world case studies.
Original languageEnglish
Number of pages17
JournalBiometrika
DOIs
Publication statusAccepted/In press - 28 Nov 2023

Keywords

  • Bayesian nonparametrics
  • Huber loss
  • Bayesian bootstrap
  • Pathwise optimization
  • Intersection-Union testing

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