Credible Uncertainty Quantification under Noise and System Model Mismatch
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910092084903936 |
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| author | Yan, Penggao Zhan, Xingqun Sun, Rui Hsu, Li-Ta |
| author_facet | Yan, Penggao Zhan, Xingqun Sun, Rui Hsu, Li-Ta |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_03311 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Credible Uncertainty Quantification under Noise and System Model Mismatch Yan, Penggao Zhan, Xingqun Sun, Rui Hsu, Li-Ta Signal Processing Information Theory 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. |
| title | Credible Uncertainty Quantification under Noise and System Model Mismatch |
| topic | Signal Processing Information Theory |
| url | https://arxiv.org/abs/2509.03311 |