Credible Uncertainty Quantification under Noise and System Model Mismatch

1) What problem is this paper solving?

Context: Filters and estimators report covariances or predictive distributions, but credibility of that uncertainty can fail under noise model mismatch (NMM) (e.g., wrong covariance scaling) or system model misspecification (SMM) (e.g., bias).
Core contribution: A unified multi-metric framework combining noncredibility index (NCI), negative log-likelihood (NLL), and energy score (ES), with an empirical location test (ELT) to detect SMM and directional probing on scaled covariances to separate NMM from SMM.
Achieved goal: Turn patterns in credibility indicators into actionable diagnoses of which modeling assumption is wrong.

2) Why is this paper important?

What changed: Single-metric checks (e.g., NEES/NCI alone) can be misleading under violations—different metrics react asymmetrically to optimism vs. pessimism vs. bias.
Problem created: Downstream fusion, planning, and safety logic depend on trustworthy uncertainty; miscalibration is hard to attribute without disentangling NMM and SMM.
Why this framework helps: NLL and ES exhibit complementary asymmetries; combining them with ELT and probing yields robust diagnosis vs. single-metric baselines.

3) How does this paper solve it?

Contribution 1: ELT (energy-distance–based) detects SMM; centering errors mitigates bias so NMM effects can be isolated.
Contribution 2: Directional probing scales reported covariances and compares NLL/ES responses to classify optimism, pessimism, and SMM.
Key result: Simulations across six credibility scenarios reach 80%–100% diagnosis accuracy and beat single-metric methods; a real UWB positioning study shows identification of coexisting pessimism and SMM where classical NEES/NCI are insufficient; complexity and scalability (including high state dimension) are analyzed.

The framework for diagnosing NMM and SMM in a unified multi-metric framework.

🎯 Takeaway: Multi-metric credibility with ELT plus directional probing is a practical validation layer when you need to know whether and why reported uncertainty is wrong.

@article{yan2026credible,
  author = {Yan, Penggao and Zhan, Xingqun and Sun, Rui and Hsu, Li-Ta},
  title = {Credible Uncertainty Quantification under Noise and System Model Mismatch},
  journal = {IEEE Transactions on Instrumentation and Measurement},
  year = {2026}
}