# Robust Bayesian inference via coarsening

arXiv: https://arxiv.org/abs/1506.06101 · HTML: https://mlsanity.com/paper/1506.06101/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jun 2015.

## Built on by (most cited first, 30 of 32)

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- [Learning the Regularization Strength for Deep Fine-Tuning via a Data-Emphasized Variational Objective](https://mlsanity.com/paper/2410.19675/) (2024)
- [Generalised Robust Bayes for Joint Inference of Model and Contamination](https://mlsanity.com/paper/2607.25665/) (2026)
- [Modeling Random Networks with Heterogeneous Reciprocity](https://mlsanity.com/paper/2308.10113/) (2023)
- [Variational empirical Bayes variable selection in high-dimensional logistic regression](https://mlsanity.com/paper/2502.10532/) (2025)
- [Correcting Mode Proportion Bias in Generalized Bayesian Inference via a Weighted Kernel Stein Discrepancy](https://mlsanity.com/paper/2503.02108/) (2025)
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## Abstract (arXiv)

The standard approach to Bayesian inference is based on the assumption that the distribution of the data belongs to the chosen model class. However, even a small violation of this assumption can have a large impact on the outcome of a Bayesian procedure. We introduce a simple, coherent approach to Bayesian inference that improves robustness to perturbations from the model: rather than condition on the data exactly, one conditions on a neighborhood of the empirical distribution. When using neighborhoods based on relative entropy estimates, the resulting "coarsened" posterior can be approximated by simply tempering the likelihood---that is, by raising it to a fractional power---thus, inference is often easily implemented with standard methods, and one can even obtain analytical solutions when using conjugate priors. Some theoretical properties are derived, and we illustrate the approach with real and simulated data, using mixture models, autoregressive models of unknown order, and variable selection in linear regression.