# Randomised Postiterations for Calibrated BayesCG

arXiv: https://arxiv.org/abs/2504.04247 · HTML: https://mlsanity.com/paper/2504.04247/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 21 references that are in the map.
- First posted on arXiv 5 Apr 2025.

## Builds on (most cited first, 7 of 7)

- [Validating Bayesian Inference Algorithms with Simulation-Based Calibration](https://mlsanity.com/paper/1804.06788/) (2018)
- [Posterior and Computational Uncertainty in Gaussian Processes](https://mlsanity.com/paper/2205.15449/) (2022)
- [Computation-Aware Kalman Filtering and Smoothing](https://mlsanity.com/paper/2405.08971/) (2024)
- [Computation-Aware Gaussian Processes: Model Selection And Linear-Time Inference](https://mlsanity.com/paper/2411.01036/) (2024)
- [Probabilistic Iterative Methods for Linear Systems](https://mlsanity.com/paper/2012.12615/) (2020)
- [Calibrated Computation-Aware Gaussian Processes](https://mlsanity.com/paper/2410.08796/) (2024)
- [Contraction rates for conjugate gradient and Lanczos approximate posteriors in Gaussian process regression](https://mlsanity.com/paper/2406.12678/) (2024)

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

- [Affine Tracing: A New Paradigm for Probabilistic Linear Solvers](https://mlsanity.com/paper/2605.10566/) (2026)

## Abstract (arXiv)

The Bayesian conjugate gradient method offers probabilistic solutions to linear systems but suffers from poor calibration, limiting its utility in uncertainty quantification tasks. Recent approaches leveraging postiterations to construct priors have improved computational properties but failed to correct calibration issues. In this work, we propose a novel randomised postiteration strategy that enhances the calibration of the BayesCG posterior while preserving its favourable convergence characteristics. We present theoretical guarantees for the improved calibration, supported by results on the distribution of posterior errors. Numerical experiments demonstrate the efficacy of the method in both synthetic and inverse problem settings, showing enhanced uncertainty quantification and better propagation of uncertainties through computational pipelines.