Uncertainty quantification: a minimum variance unbiased (joint) estimator of the non-normalized Sobol’ indices
Abstract Often, uncertainty quantification is followed by the computation of sensitivity indices of input factors. Variance-based sensitivity analysis and multivariate sensitivity analysis (MSA) aim to apportion the variability of the model output(s) into input factors and their interactions. Sobol’...
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Gespeichert in:
| Autor*in: |
Lamboni, Matieyendou [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2018 |
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| Schlagwörter: |
First-order index and total indices |
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| Anmerkung: |
© Springer-Verlag GmbH Germany, part of Springer Nature 2018 |
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| Übergeordnetes Werk: |
Enthalten in: Statistical papers - Springer Berlin Heidelberg, 1988, 61(2018), 5 vom: 24. Mai, Seite 1939-1970 |
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| Übergeordnetes Werk: |
volume:61 ; year:2018 ; number:5 ; day:24 ; month:05 ; pages:1939-1970 |
| Links: |
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| DOI / URN: |
10.1007/s00362-018-1010-4 |
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| 520 | |a Abstract Often, uncertainty quantification is followed by the computation of sensitivity indices of input factors. Variance-based sensitivity analysis and multivariate sensitivity analysis (MSA) aim to apportion the variability of the model output(s) into input factors and their interactions. Sobol’ indices (first-order and total indices), which quantify the effects of input factor(s), serve as a practical tool to assess interactions among input factors, the order of interactions, and the magnitude of interactions. In this paper, we investigate a novel way of estimating both the first-order and total indices based on U-statistics, including the statistical properties of the new estimator. First, we provide a minimum variance unbiased estimator of the non-normalized Sobol’ indices as well as its optimal rate of convergence and its asymptotic distribution. Second, we derive a joint estimator of Sobol’ indices, its consistency and its asymptotic distribution, and third, we demonstrate the applicability of these results by means of numerical tests. The new estimator allows for improving the estimation of Sobol’ indices for some degrees of the kernel. | ||
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10.1007/s00362-018-1010-4 doi (DE-627)OLC211954977X (DE-He213)s00362-018-1010-4-p DE-627 ger DE-627 rakwb eng 300 330 510 VZ Lamboni, Matieyendou verfasserin aut Uncertainty quantification: a minimum variance unbiased (joint) estimator of the non-normalized Sobol’ indices 2018 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag GmbH Germany, part of Springer Nature 2018 Abstract Often, uncertainty quantification is followed by the computation of sensitivity indices of input factors. Variance-based sensitivity analysis and multivariate sensitivity analysis (MSA) aim to apportion the variability of the model output(s) into input factors and their interactions. Sobol’ indices (first-order and total indices), which quantify the effects of input factor(s), serve as a practical tool to assess interactions among input factors, the order of interactions, and the magnitude of interactions. In this paper, we investigate a novel way of estimating both the first-order and total indices based on U-statistics, including the statistical properties of the new estimator. First, we provide a minimum variance unbiased estimator of the non-normalized Sobol’ indices as well as its optimal rate of convergence and its asymptotic distribution. Second, we derive a joint estimator of Sobol’ indices, its consistency and its asymptotic distribution, and third, we demonstrate the applicability of these results by means of numerical tests. The new estimator allows for improving the estimation of Sobol’ indices for some degrees of the kernel. First-order index and total indices MVU estimators Sensitivity and uncertainty analysis U-statistics Enthalten in Statistical papers Springer Berlin Heidelberg, 1988 61(2018), 5 vom: 24. Mai, Seite 1939-1970 (DE-627)129572292 (DE-600)227641-0 (DE-576)015069486 0932-5026 nnns volume:61 year:2018 number:5 day:24 month:05 pages:1939-1970 https://doi.org/10.1007/s00362-018-1010-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_11 GBV_ILN_26 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2018 GBV_ILN_4277 GBV_ILN_4319 GBV_ILN_4326 AR 61 2018 5 24 05 1939-1970 |
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10.1007/s00362-018-1010-4 doi (DE-627)OLC211954977X (DE-He213)s00362-018-1010-4-p DE-627 ger DE-627 rakwb eng 300 330 510 VZ Lamboni, Matieyendou verfasserin aut Uncertainty quantification: a minimum variance unbiased (joint) estimator of the non-normalized Sobol’ indices 2018 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag GmbH Germany, part of Springer Nature 2018 Abstract Often, uncertainty quantification is followed by the computation of sensitivity indices of input factors. Variance-based sensitivity analysis and multivariate sensitivity analysis (MSA) aim to apportion the variability of the model output(s) into input factors and their interactions. Sobol’ indices (first-order and total indices), which quantify the effects of input factor(s), serve as a practical tool to assess interactions among input factors, the order of interactions, and the magnitude of interactions. In this paper, we investigate a novel way of estimating both the first-order and total indices based on U-statistics, including the statistical properties of the new estimator. First, we provide a minimum variance unbiased estimator of the non-normalized Sobol’ indices as well as its optimal rate of convergence and its asymptotic distribution. Second, we derive a joint estimator of Sobol’ indices, its consistency and its asymptotic distribution, and third, we demonstrate the applicability of these results by means of numerical tests. The new estimator allows for improving the estimation of Sobol’ indices for some degrees of the kernel. First-order index and total indices MVU estimators Sensitivity and uncertainty analysis U-statistics Enthalten in Statistical papers Springer Berlin Heidelberg, 1988 61(2018), 5 vom: 24. Mai, Seite 1939-1970 (DE-627)129572292 (DE-600)227641-0 (DE-576)015069486 0932-5026 nnns volume:61 year:2018 number:5 day:24 month:05 pages:1939-1970 https://doi.org/10.1007/s00362-018-1010-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_11 GBV_ILN_26 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2018 GBV_ILN_4277 GBV_ILN_4319 GBV_ILN_4326 AR 61 2018 5 24 05 1939-1970 |
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10.1007/s00362-018-1010-4 doi (DE-627)OLC211954977X (DE-He213)s00362-018-1010-4-p DE-627 ger DE-627 rakwb eng 300 330 510 VZ Lamboni, Matieyendou verfasserin aut Uncertainty quantification: a minimum variance unbiased (joint) estimator of the non-normalized Sobol’ indices 2018 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag GmbH Germany, part of Springer Nature 2018 Abstract Often, uncertainty quantification is followed by the computation of sensitivity indices of input factors. Variance-based sensitivity analysis and multivariate sensitivity analysis (MSA) aim to apportion the variability of the model output(s) into input factors and their interactions. Sobol’ indices (first-order and total indices), which quantify the effects of input factor(s), serve as a practical tool to assess interactions among input factors, the order of interactions, and the magnitude of interactions. In this paper, we investigate a novel way of estimating both the first-order and total indices based on U-statistics, including the statistical properties of the new estimator. First, we provide a minimum variance unbiased estimator of the non-normalized Sobol’ indices as well as its optimal rate of convergence and its asymptotic distribution. Second, we derive a joint estimator of Sobol’ indices, its consistency and its asymptotic distribution, and third, we demonstrate the applicability of these results by means of numerical tests. The new estimator allows for improving the estimation of Sobol’ indices for some degrees of the kernel. First-order index and total indices MVU estimators Sensitivity and uncertainty analysis U-statistics Enthalten in Statistical papers Springer Berlin Heidelberg, 1988 61(2018), 5 vom: 24. Mai, Seite 1939-1970 (DE-627)129572292 (DE-600)227641-0 (DE-576)015069486 0932-5026 nnns volume:61 year:2018 number:5 day:24 month:05 pages:1939-1970 https://doi.org/10.1007/s00362-018-1010-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_11 GBV_ILN_26 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2018 GBV_ILN_4277 GBV_ILN_4319 GBV_ILN_4326 AR 61 2018 5 24 05 1939-1970 |
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10.1007/s00362-018-1010-4 doi (DE-627)OLC211954977X (DE-He213)s00362-018-1010-4-p DE-627 ger DE-627 rakwb eng 300 330 510 VZ Lamboni, Matieyendou verfasserin aut Uncertainty quantification: a minimum variance unbiased (joint) estimator of the non-normalized Sobol’ indices 2018 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag GmbH Germany, part of Springer Nature 2018 Abstract Often, uncertainty quantification is followed by the computation of sensitivity indices of input factors. Variance-based sensitivity analysis and multivariate sensitivity analysis (MSA) aim to apportion the variability of the model output(s) into input factors and their interactions. Sobol’ indices (first-order and total indices), which quantify the effects of input factor(s), serve as a practical tool to assess interactions among input factors, the order of interactions, and the magnitude of interactions. In this paper, we investigate a novel way of estimating both the first-order and total indices based on U-statistics, including the statistical properties of the new estimator. First, we provide a minimum variance unbiased estimator of the non-normalized Sobol’ indices as well as its optimal rate of convergence and its asymptotic distribution. Second, we derive a joint estimator of Sobol’ indices, its consistency and its asymptotic distribution, and third, we demonstrate the applicability of these results by means of numerical tests. The new estimator allows for improving the estimation of Sobol’ indices for some degrees of the kernel. First-order index and total indices MVU estimators Sensitivity and uncertainty analysis U-statistics Enthalten in Statistical papers Springer Berlin Heidelberg, 1988 61(2018), 5 vom: 24. Mai, Seite 1939-1970 (DE-627)129572292 (DE-600)227641-0 (DE-576)015069486 0932-5026 nnns volume:61 year:2018 number:5 day:24 month:05 pages:1939-1970 https://doi.org/10.1007/s00362-018-1010-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_11 GBV_ILN_26 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2018 GBV_ILN_4277 GBV_ILN_4319 GBV_ILN_4326 AR 61 2018 5 24 05 1939-1970 |
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10.1007/s00362-018-1010-4 doi (DE-627)OLC211954977X (DE-He213)s00362-018-1010-4-p DE-627 ger DE-627 rakwb eng 300 330 510 VZ Lamboni, Matieyendou verfasserin aut Uncertainty quantification: a minimum variance unbiased (joint) estimator of the non-normalized Sobol’ indices 2018 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag GmbH Germany, part of Springer Nature 2018 Abstract Often, uncertainty quantification is followed by the computation of sensitivity indices of input factors. Variance-based sensitivity analysis and multivariate sensitivity analysis (MSA) aim to apportion the variability of the model output(s) into input factors and their interactions. Sobol’ indices (first-order and total indices), which quantify the effects of input factor(s), serve as a practical tool to assess interactions among input factors, the order of interactions, and the magnitude of interactions. In this paper, we investigate a novel way of estimating both the first-order and total indices based on U-statistics, including the statistical properties of the new estimator. First, we provide a minimum variance unbiased estimator of the non-normalized Sobol’ indices as well as its optimal rate of convergence and its asymptotic distribution. Second, we derive a joint estimator of Sobol’ indices, its consistency and its asymptotic distribution, and third, we demonstrate the applicability of these results by means of numerical tests. The new estimator allows for improving the estimation of Sobol’ indices for some degrees of the kernel. First-order index and total indices MVU estimators Sensitivity and uncertainty analysis U-statistics Enthalten in Statistical papers Springer Berlin Heidelberg, 1988 61(2018), 5 vom: 24. Mai, Seite 1939-1970 (DE-627)129572292 (DE-600)227641-0 (DE-576)015069486 0932-5026 nnns volume:61 year:2018 number:5 day:24 month:05 pages:1939-1970 https://doi.org/10.1007/s00362-018-1010-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_11 GBV_ILN_26 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2018 GBV_ILN_4277 GBV_ILN_4319 GBV_ILN_4326 AR 61 2018 5 24 05 1939-1970 |
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Uncertainty quantification: a minimum variance unbiased (joint) estimator of the non-normalized Sobol’ indices |
| abstract |
Abstract Often, uncertainty quantification is followed by the computation of sensitivity indices of input factors. Variance-based sensitivity analysis and multivariate sensitivity analysis (MSA) aim to apportion the variability of the model output(s) into input factors and their interactions. Sobol’ indices (first-order and total indices), which quantify the effects of input factor(s), serve as a practical tool to assess interactions among input factors, the order of interactions, and the magnitude of interactions. In this paper, we investigate a novel way of estimating both the first-order and total indices based on U-statistics, including the statistical properties of the new estimator. First, we provide a minimum variance unbiased estimator of the non-normalized Sobol’ indices as well as its optimal rate of convergence and its asymptotic distribution. Second, we derive a joint estimator of Sobol’ indices, its consistency and its asymptotic distribution, and third, we demonstrate the applicability of these results by means of numerical tests. The new estimator allows for improving the estimation of Sobol’ indices for some degrees of the kernel. © Springer-Verlag GmbH Germany, part of Springer Nature 2018 |
| abstractGer |
Abstract Often, uncertainty quantification is followed by the computation of sensitivity indices of input factors. Variance-based sensitivity analysis and multivariate sensitivity analysis (MSA) aim to apportion the variability of the model output(s) into input factors and their interactions. Sobol’ indices (first-order and total indices), which quantify the effects of input factor(s), serve as a practical tool to assess interactions among input factors, the order of interactions, and the magnitude of interactions. In this paper, we investigate a novel way of estimating both the first-order and total indices based on U-statistics, including the statistical properties of the new estimator. First, we provide a minimum variance unbiased estimator of the non-normalized Sobol’ indices as well as its optimal rate of convergence and its asymptotic distribution. Second, we derive a joint estimator of Sobol’ indices, its consistency and its asymptotic distribution, and third, we demonstrate the applicability of these results by means of numerical tests. The new estimator allows for improving the estimation of Sobol’ indices for some degrees of the kernel. © Springer-Verlag GmbH Germany, part of Springer Nature 2018 |
| abstract_unstemmed |
Abstract Often, uncertainty quantification is followed by the computation of sensitivity indices of input factors. Variance-based sensitivity analysis and multivariate sensitivity analysis (MSA) aim to apportion the variability of the model output(s) into input factors and their interactions. Sobol’ indices (first-order and total indices), which quantify the effects of input factor(s), serve as a practical tool to assess interactions among input factors, the order of interactions, and the magnitude of interactions. In this paper, we investigate a novel way of estimating both the first-order and total indices based on U-statistics, including the statistical properties of the new estimator. First, we provide a minimum variance unbiased estimator of the non-normalized Sobol’ indices as well as its optimal rate of convergence and its asymptotic distribution. Second, we derive a joint estimator of Sobol’ indices, its consistency and its asymptotic distribution, and third, we demonstrate the applicability of these results by means of numerical tests. The new estimator allows for improving the estimation of Sobol’ indices for some degrees of the kernel. © Springer-Verlag GmbH Germany, part of Springer Nature 2018 |
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| container_issue |
5 |
| title_short |
Uncertainty quantification: a minimum variance unbiased (joint) estimator of the non-normalized Sobol’ indices |
| url |
https://doi.org/10.1007/s00362-018-1010-4 |
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| doi_str |
10.1007/s00362-018-1010-4 |
| up_date |
2024-07-04T01:26:38.034Z |
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