Generalised Robust Bayes for Joint Inference of Model and Contamination

• URL: http://arxiv.org/abs/2607.25665v1
• Date: Tue, 28 Jul 2026 12:50:04 GMT
• Title: Generalised Robust Bayes for Joint Inference of Model and Contamination
• Abstract summary: Generalised Bayesian inference (GBI) has emerged as a compelling robust alternative to standard Bayesian inference.<n>This paper introduces Hlder-Bayes, a GBI framework for joint inference of the model parameter and the contamination proportion.<n> Empirical evaluations demonstrate that Hlder-Bayes provides robust parameter inference, contamination-level recovery, and uncertainty-aware outlier detection.
• Score: 12.194688106820815
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Generalised Bayesian inference (GBI) has emerged as a compelling robust alternative to standard Bayesian inference, mitigating sensitivity to data contamination by replacing the log-likelihood with a robust loss or divergence. However, existing robust GBI frameworks typically provide only qualitative robustness: while they can make posterior inference less sensitive to contamination, they lack an intrinsic mechanism to quantify the contamination proportion or identify anomalous observations. This paper introduces Hölder-Bayes, a GBI framework for joint inference of the model parameter and the contamination proportion. We construct a generalised joint posterior over both model and contamination parameter by applying the Hölder divergence to a scaled model density. Theoretically, we establish global bias-robustness via the uniform boundedness of the posterior influence function, derive a finite-sample excess-risk bound, and prove a Bernstein--von Mises approximation together with interpretable contamination-induced bias bounds under a heavy-contamination regime. We further show that, for the Hölder posterior, temperature calibration admits a direct interpretation as affine volume scaling of the data space. The resulting posterior yields a self-contained probabilistic mechanism for outlier detection: posterior uncertainty in both the model parameter and the contamination proportion is propagated to observation-level Frequency-of-Detection scores, without requiring an external anomaly-score threshold. Empirical evaluations demonstrate that Hölder-Bayes provides robust parameter inference, contamination-level recovery, and uncertainty-aware outlier detection.

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