# Credible Uncertainty Quantification under Noise and System Model Mismatch

arXiv: https://arxiv.org/abs/2509.03311 · HTML: https://mlsanity.com/paper/2509.03311/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Sep 2025.

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

- [CredibleDFGO: Differentiable Factor Graph Optimization with Credibility Supervision](https://mlsanity.com/paper/2605.06100/) (2026)

## Abstract (arXiv)

State estimators often provide self-assessed uncertainty metrics, such as covariance matrices, whose credibility is critical for downstream tasks. However, these self-assessments can be misleading due to underlying modeling violations like noise model mismatch (NMM) or system model misspecification (SMM). This letter addresses this problem by developing a unified, multi-metric framework that integrates noncredibility index (NCI), negative log-likelihood (NLL), and energy score (ES) metrics, featuring an empirical location test (ELT) to detect system model bias and a directional probing technique that uses the metrics' asymmetric sensitivities to distinguish NMM from SMM. Monte Carlo simulations reveal that the proposed method achieves excellent diagnosis accuracy (80-100%) and significantly outperforms single-metric diagnosis methods. The effectiveness of the proposed method is further validated on a real-world UWB positioning dataset. This framework provides a practical tool for turning patterns of credibility indicators into actionable diagnoses of model deficiencies.