Sobol' Matrices For Multi-Output Models With Quantified Uncertainty
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917964831260672 |
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| author | Milton, Robert A. Brown, Solomon F. |
| author_facet | Milton, Robert A. Brown, Solomon F. |
| contents | Variance based global sensitivity analysis measures the relevance of inputs to a single output using Sobol' indices. This paper extends the definition in a natural way to multiple outputs, directly measuring the relevance of inputs to the linkages between outputs in a correlation-like matrix of indices. The usual Sobol' indices constitute the diagonal of this matrix. Existence, uniqueness and uncertainty quantification are established by developing the indices from a putative multi-output model with quantified uncertainty. Sobol' matrices and their standard errors are related to the moments of the multi-output model, to enable calculation. These are benchmarked numerically against test functions (with added noise) whose Sobol' matrices are calculated analytically. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_04602 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sobol' Matrices For Multi-Output Models With Quantified Uncertainty Milton, Robert A. Brown, Solomon F. Statistics Theory 60G07, 60G15, 62J10, 62H99 Variance based global sensitivity analysis measures the relevance of inputs to a single output using Sobol' indices. This paper extends the definition in a natural way to multiple outputs, directly measuring the relevance of inputs to the linkages between outputs in a correlation-like matrix of indices. The usual Sobol' indices constitute the diagonal of this matrix. Existence, uniqueness and uncertainty quantification are established by developing the indices from a putative multi-output model with quantified uncertainty. Sobol' matrices and their standard errors are related to the moments of the multi-output model, to enable calculation. These are benchmarked numerically against test functions (with added noise) whose Sobol' matrices are calculated analytically. |
| title | Sobol' Matrices For Multi-Output Models With Quantified Uncertainty |
| topic | Statistics Theory 60G07, 60G15, 62J10, 62H99 |
| url | https://arxiv.org/abs/2501.04602 |