# Bayesian inference with sources of uncertainty: from confidence modelling to sparse estimation

arXiv: https://arxiv.org/abs/2605.03134 · HTML: https://mlsanity.com/paper/2605.03134/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 31 references that are in the map.
- First posted on arXiv 4 May 2026.

## Builds on (most cited first, 8 of 8)

- [Black Box Variational Inference](https://mlsanity.com/paper/1401.0118/) (2013)
- [A General Framework for Updating Belief Distributions](https://mlsanity.com/paper/1306.6430/) (2013)
- [The Bayesian Learning Rule](https://mlsanity.com/paper/2107.04562/) (2021)
- [Inconsistency of Bayesian Inference for Misspecified Linear Models, and a Proposal for Repairing It](https://mlsanity.com/paper/1412.3730/) (2014)
- [Model Selection in Bayesian Neural Networks via Horseshoe Priors](https://mlsanity.com/paper/1705.10388/) (2017)
- [Assigning a value to a power likelihood in a general Bayesian model](https://mlsanity.com/paper/1701.08515/) (2017)
- [Structured Variational Learning of Bayesian Neural Networks with Horseshoe Priors](https://mlsanity.com/paper/1806.05975/) (2018)
- [Robust Bayesian inference via coarsening](https://mlsanity.com/paper/1506.06101/) (2015)

## Abstract (arXiv)

We introduce a general framework that extends Bayesian inference by allowing the researcher to explicitly encode confidence in each source of uncertainty within the model. This mechanism provides a new handle for model design and regularisation control. Building on this framework, we develop a general approach for inducing sparsity in statistical models and illustrate its use in linear and logistic regression, as well as in Bayesian neural networks.