Title -- Familial inference: Tests for hypotheses on a family of centers
Abstract -- Many scientific disciplines face a replicability crisis. While these crises have many drivers, we focus on one.
Statistical hypotheses are translations of scientific hypotheses into statements about one or more distributions.
The most basic tests focus on the centers of the distributions. Such tests implicitly assume a specific center, e.g.,
the mean or the median. Yet, scientific hypotheses do not always specify a particular center.
This ambiguity leaves a gap between scientific theory and statistical practice that can lead to rejection of a true null.
The gap is compounded when we consider deficiencies in the formal statistical model.
Rather than testing a single center, we propose testing a family of plausible centers,
such as those induced by the Huber loss function (the Huber family).
Each center in the family generates a point null hypothesis and the resulting family of hypotheses constitutes a
familial null hypothesis. A Bayesian nonparametric procedure is devised to test the familial null.
Implementation for the Huber family is facilitated by a novel pathwise optimization routine.
Along the way, we visit the question of what it means to be the center of a distribution.
The favorable properties of the new test are demonstrated theoretically and in case studies.
This is joint work with Ryan Thompson (University of New South Wales),
Catherine Forbes (Monash University), and Mario Peruggia (The Ohio State University).
Zoom link: LINK