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arXiv Statistics ML By Masahiro Fujisawa, Masaki Adachi, Takuo Matsubara

Generalised Robust Bayes for Joint Inference of Model and Contamination

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The paper introduces H"older--Bayes, a robust generalised Bayesian framework that jointly infers model parameters and the proportion of contamination without specifying an outlier distribution. By applying the H"older divergence to a scaled model, each posterior draw identifies observations least compatible with the fitted model, and averaging these selections propagates uncertainty to outlier‑detection scores. The authors provide theoretical guarantees—including uniform boundedness of the posterior influence function, an $n^{-1/2}$ bound on posterior‑averaged excess risk, and a Bernstein–von Mises theorem—while also demonstrating practical performance through simulations and real‑data experiments.

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