arXiv:2607.25665v2 Announce Type: replace-cross Abstract: Robust generalised Bayesian methods protect parameter inference from contamination but do not generally infer its proportion or identify individual outliers. We propose H\"older--Bayes, which applies the H\"older 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.