Generalised Robust Bayes for Joint Inference of Model and Contamination
Abstract
Robust generalised Bayesian methods protect parameter inference from contamination but do not generally infer its proportion or identify individual outliers. We propose Hölder--Bayes, which applies the Hölder divergence to a scaled model to construct a joint generalised posterior over model parameters and the contamination proportion, without specifying an outlier distribution. Each posterior draw flags a corresponding number of observations least compatible with the fitted model; averaging selections propagates joint uncertainty to outlier-detection scores. Under fixed, non-negligible contamination, we establish uniform boundedness of the posterior influence function, a finite-sample n−1/2 bound on posterior-averaged excess risk, and a Bernstein--von Mises theorem. Tail overlap between the outlier distribution and the fitted model controls the population risk minimiser's bias and the associated change in limiting posterior covariance. Interpreting the posterior temperature as an affine volume scaling yields a closed-form, data-driven choice. Simulations and real-data experiments demonstrate robust estimation, contamination-proportion recovery, and posterior-guided data cleaning.
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BibTeX
@misc{fujisawa2026generalised,
title = {{Generalised Robust Bayes for Joint Inference of Model and Contamination}},
author = {Masahiro Fujisawa and Masaki Adachi and Takuo Matsubara},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.25665},
eprint = {2607.25665},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.25665},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Generalised Robust Bayes for Joint Inference of Model and Contamination
AU - Masahiro Fujisawa
AU - Masaki Adachi
AU - Takuo Matsubara
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2607.25665
UR - https://arxiv.org/abs/2607.25665
AB - Robust generalised Bayesian methods protect parameter inference from contamination but do not generally infer its proportion or identify individual outliers. We propose Hölder--Bayes, which applies the Hölder divergence to a scaled model to construct a joint generalised posterior over model parameters and the contamination proportion, without specifying an outlier distribution. Each posterior draw flags a corresponding number of observations least compatible with the fitted model; averaging selections propagates joint uncertainty to outlier-detection scores. Under fixed, non-negligible contamination, we establish uniform boundedness of the posterior influence function, a finite-sample n^−1/2 bound on posterior-averaged excess risk, and a Bernstein--von Mises theorem. Tail overlap between the outlier distribution and the fitted model controls the population risk minimiser's bias and the associated change in limiting posterior covariance. Interpreting the posterior temperature as an affine volume scaling yields a closed-form, data-driven choice. Simulations and real-data experiments demonstrate robust estimation, contamination-proportion recovery, and posterior-guided data cleaning.
ER -