# Reliable Bayesian Inference in Misspecified Models

arXiv: https://arxiv.org/abs/2302.06031 · HTML: https://mlsanity.com/paper/2302.06031/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Feb 2023.

## Built on by (most cited first, 4 of 4)

- [Addressing Misspecification in Simulation-based Inference through Data-driven Calibration](https://mlsanity.com/paper/2405.08719/) (2024)
- [Robust and Conjugate Gaussian Process Regression](https://mlsanity.com/paper/2311.00463/) (2023)
- [Representative, Informative, and De-Amplifying: Requirements for Robust Bayesian Active Learning under Model Misspecification](https://mlsanity.com/paper/2506.07805/) (2025)
- [Misspecifying non-compensatory as compensatory IRT: analysis of estimated skills and variance](https://mlsanity.com/paper/2507.15222/) (2025)

## Abstract (arXiv)

We provide a general solution to a fundamental open problem in Bayesian inference, namely poor uncertainty quantification, from a frequency standpoint, of Bayesian methods in misspecified models. While existing solutions are based on explicit Gaussian approximations of the posterior, or computationally onerous post-processing procedures, we demonstrate that correct uncertainty quantification can be achieved by replacing the usual posterior with an intuitive approximate posterior. Critically, our solution is applicable to likelihood-based, and generalized, posteriors as well as cases where the likelihood is intractable and must be estimated. We formally demonstrate the reliable uncertainty quantification of our proposed approach, and show that valid uncertainty quantification is not an asymptotic result but occurs even in small samples. We illustrate this approach through a range of examples, including linear, and generalized, mixed effects models.