# Generalised Robust Bayes for Joint Inference of Model and Contamination

arXiv: https://arxiv.org/abs/2607.25665 · HTML: https://mlsanity.com/paper/2607.25665/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 43 references that are in the map.
- First posted on arXiv 28 Jul 2026.

## Builds on (most cited first, 11 of 11)

- [A General Framework for Updating Belief Distributions](https://mlsanity.com/paper/1306.6430/) (2013)
- [Inconsistency of Bayesian Inference for Misspecified Linear Models, and a Proposal for Repairing It](https://mlsanity.com/paper/1412.3730/) (2014)
- [Robust Generalised Bayesian Inference for Intractable Likelihoods](https://mlsanity.com/paper/2104.07359/) (2021)
- [Assigning a value to a power likelihood in a general Bayesian model](https://mlsanity.com/paper/1701.08515/) (2017)
- [General Bayesian Updating and the Loss-Likelihood Bootstrap](https://mlsanity.com/paper/1709.07616/) (2017)
- [Robust Bayesian inference via coarsening](https://mlsanity.com/paper/1506.06101/) (2015)
- [A comparison of learning rate selection methods in generalized Bayesian inference](https://mlsanity.com/paper/2012.11349/) (2020)
- [Minimum Covariance Determinant and Extensions](https://mlsanity.com/paper/1709.07045/) (2017)
- [Generalised Bayesian Inference for Discrete Intractable Likelihood](https://mlsanity.com/paper/2206.08420/) (2022)
- [Robust and Conjugate Spatio-Temporal Gaussian Processes](https://mlsanity.com/paper/2502.02450/) (2025)
- [Scalable Valuation of Human Feedback through Provably Robust Model Alignment](https://mlsanity.com/paper/2505.17859/) (2025)

## Built on by (most cited first, 1 of 1)

- [Open-ended Scientific Discovery with Possibilistic Reasoning](https://mlsanity.com/paper/2610.11289/) (2026)

## Abstract (arXiv)

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 H"older-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 H"older 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 H"older 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 H"older-Bayes provides robust parameter inference, contamination-level recovery, and uncertainty-aware outlier detection.