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Journal articles on the topic 'Sensitivity indices'

Author: Grafiati

Published: 9 March 2023

Last updated: 11 March 2023

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1

Lamboni, Matieyendou. "Derivative-based generalized sensitivity indices and Sobol’ indices." Mathematics and Computers in Simulation 170 (April 2020): 236–56. http://dx.doi.org/10.1016/j.matcom.2019.10.017.

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2

Xu, Chonggang, and George Zdzislaw Gertner. "Reliability of global sensitivity indices." Journal of Statistical Computation and Simulation 81, no. 12 (December 2011): 1939–69. http://dx.doi.org/10.1080/00949655.2010.509317.

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3

Da Veiga, Sébastien, and Fabrice Gamboa. "Efficient estimation of sensitivity indices." Journal of Nonparametric Statistics 25, no. 3 (September 2013): 573–95. http://dx.doi.org/10.1080/10485252.2013.784762.

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4

Gamboa, Fabrice, Alexandre Janon, Thierry Klein, and Agnès Lagnoux. "Sensitivity indices for multivariate outputs." Comptes Rendus Mathematique 351, no. 7-8 (April 2013): 307–10. http://dx.doi.org/10.1016/j.crma.2013.04.016.

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5

Izsák, János. "Sensitivity Profiles of Diversity Indices." Biometrical Journal 38, no. 8 (1996): 921–30. http://dx.doi.org/10.1002/bimj.4710380804.

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6

MacArthur, Lauren A. "Dust Sensitivity of Absorption‐Line Indices." Astrophysical Journal 623, no. 2 (April 20, 2005): 795–814. http://dx.doi.org/10.1086/428827.

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7

Janon, Alexandre, Maëlle Nodet, and Clémentine Prieur. "Certified metamodels for sensitivity indices estimation." ESAIM: Proceedings 35 (March 2012): 234–38. http://dx.doi.org/10.1051/proc/201235020.

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8

Salome, C. M., N. J. Brown, H. K. Reddel, W. Xuan, and G. B. Marks. "Indices of bronchial reactivity and sensitivity." Thorax 66, no. 3 (October 27, 2010): 265–66. http://dx.doi.org/10.1136/thx.2010.151639.

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9

Chung, C. Y., C. T. Tse, R. Niu, and K. W. Wang. "PSS Design by Probabilistic Sensitivity Indices." IEEE Power Engineering Review 22, no. 7 (July 2002): 56. http://dx.doi.org/10.1109/mper.2002.4312394.

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10

Lasersohn, Peter. "Non-World Indices and Assessment-Sensitivity." Inquiry 56, no. 2-3 (April 2013): 122–48. http://dx.doi.org/10.1080/0020174x.2013.784463.

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11

Maume-Deschamps, Véronique, and Ibrahima Niang. "Estimation of quantile oriented sensitivity indices." Statistics & Probability Letters 134 (March 2018): 122–27. http://dx.doi.org/10.1016/j.spl.2017.10.019.

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12

Glen, Graham, and Kristin Isaacs. "Estimating Sobol sensitivity indices using correlations." Environmental Modelling & Software 37 (November 2012): 157–66. http://dx.doi.org/10.1016/j.envsoft.2012.03.014.

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13

Sanderson, Benjamin. "Relating climate sensitivity indices to projection uncertainty." Earth System Dynamics 11, no. 3 (August 4, 2020): 721–35. http://dx.doi.org/10.5194/esd-11-721-2020.

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Abstract. Can we summarize uncertainties in global response to greenhouse gas forcing with a single number? Here, we assess the degree to which traditional metrics are related to future warming indices using an ensemble of simple climate models together with results from the Coupled Model Intercomparison Project phases 5 and 6 (CMIP5 and CMIP6). We consider effective climate sensitivity (EffCS), transient climate response (TCR) at CO2 quadrupling (T140) and a proposed simple metric of temperature change 140 years after a quadrupling of carbon dioxide (A140). In a perfectly equilibrated model, future temperatures under RCP8.5 (Representative Concentration Pathway 8.5) are almost perfectly described by T140, whereas in a mitigation scenario such as RCP2.6, both EffCS and T140 are found to be poor predictors of 21st century warming, and future temperatures are better correlated with A140. We show further that T140 and EffCS calculated in full CMIP simulations are subject to errors arising from control model drift and internal variability, with greater relative errors in estimation for T140. As such, if starting from a non-equilibrated state, measured values of effective climate sensitivity can be better correlated with true TCR than measured values of TCR itself. We propose that this could be an explanatory factor in the previously noted surprising result that EffCS is a better predictor than TCR of future transient warming under RCP8.5.

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14

Paes de Camargo, Marcelo B., and Kenneth G. Hubbard. "Drought Sensitivity Indices for a Sorghum Crop." Journal of Production Agriculture 12, no. 2 (April 1999): 312–16. http://dx.doi.org/10.2134/jpa1999.0312.

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15

Owen, Art B. "Better estimation of small sobol' sensitivity indices." ACM Transactions on Modeling and Computer Simulation 23, no. 2 (May 2013): 1–17. http://dx.doi.org/10.1145/2457459.2457460.

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16

Simpson-Porco, John William, and Francesco Bullo. "Distributed Monitoring of Voltage Collapse Sensitivity Indices." IEEE Transactions on Smart Grid 7, no. 4 (July 2016): 1979–88. http://dx.doi.org/10.1109/tsg.2016.2533319.

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17

Broto, Baptiste, François Bachoc, Marine Depecker, and Jean-Marc Martinez. "Sensitivity indices for independent groups of variables." Mathematics and Computers in Simulation 163 (September 2019): 19–31. http://dx.doi.org/10.1016/j.matcom.2019.02.008.

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18

Perrin, G., and G. Defaux. "Efficient Evaluation of Reliability-Oriented Sensitivity Indices." Journal of Scientific Computing 79, no. 3 (January 8, 2019): 1433–55. http://dx.doi.org/10.1007/s10915-018-00898-8.

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19

Muniyappa, Ranganath, Brian A. Irving, Uma S. Unni, William M. Briggs, K. Sreekumaran Nair, Michael J. Quon, and Anura V. Kurpad. "Limited predictive ability of surrogate indices of insulin sensitivity/resistance in Asian-Indian men." American Journal of Physiology-Endocrinology and Metabolism 299, no. 6 (December 2010): E1106—E1112. http://dx.doi.org/10.1152/ajpendo.00454.2010.

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Insulin resistance is highly prevalent in Asian Indians and contributes to worldwide public health problems, including diabetes and related disorders. Surrogate measurements of insulin sensitivity/resistance are used frequently to study Asian Indians, but these are not formally validated in this population. In this study, we compared the ability of simple surrogate indices to accurately predict insulin sensitivity as determined by the reference glucose clamp method. In this cross-sectional study of Asian-Indian men ( n = 70), we used a calibration model to assess the ability of simple surrogate indices for insulin sensitivity [quantitative insulin sensitivity check index (QUICKI), homeostasis model assessment (HOMA2-IR), fasting insulin-to-glucose ratio (FIGR), and fasting insulin (FI)] to predict an insulin sensitivity index derived from the reference glucose clamp method (SIClamp). Predictive accuracy was assessed by both root mean squared error (RMSE) of prediction as well as leave-one-out cross-validation-type RMSE of prediction (CVPE). QUICKI, FIGR, and FI, but not HOMA2-IR, had modest linear correlations with SIClamp (QUICKI: r = 0.36; FIGR: r = −0.36; FI: r = −0.27; P < 0.05). No significant differences were noted among CVPE or RMSE from any of the surrogate indices when compared with QUICKI. Surrogate measurements of insulin sensitivity/resistance such as QUICKI, FIGR, and FI are easily obtainable in large clinical studies, but these may only be useful as secondary outcome measurements in assessing insulin sensitivity/resistance in clinical studies of Asian Indians.

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20

Kala, Zdeněk. "Global Sensitivity Analysis of Quantiles: New Importance Measure Based on Superquantiles and Subquantiles." Symmetry 13, no. 2 (February 4, 2021): 263. http://dx.doi.org/10.3390/sym13020263.

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The article introduces quantile deviation l as a new sensitivity measure based on the difference between superquantile and subquantile. New global sensitivity indices based on the square of l are presented. The proposed sensitivity indices are compared with quantile-oriented sensitivity indices subordinated to contrasts and classical Sobol sensitivity indices. The comparison is performed in a case study using a non-linear mathematical function, the output of which represents the elastic resistance of a slender steel member under compression. The steel member has random imperfections that reduce its load-carrying capacity. The member length is a deterministic parameter that significantly changes the sensitivity of the output resistance to the random effects of input imperfections. The comparison of the results of three types of global sensitivity analyses shows the rationality of the new quantile-oriented sensitivity indices, which have good properties similar to classical Sobol indices. Sensitivity indices subordinated to contrasts are the least comprehensible because they exhibit the strongest interaction effects between inputs. However, using total indices, all three types of sensitivity analyses lead to approximately the same conclusions. The similarity of the results of two quantile-oriented and Sobol sensitivity analysis confirms that Sobol sensitivity analysis is empathetic to the structural reliability and that the variance is one of the important characteristics significantly influencing the low quantile of resistance.

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21

Zhou, Huai Zhi, Dong Xuan Wei, and Hong Zhi Yang. "Quantitative Analysis Indices of Highway Landscape Design." Applied Mechanics and Materials 744-746 (March 2015): 1283–87. http://dx.doi.org/10.4028/www.scientific.net/amm.744-746.1283.

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In this paper, the problems existing in highway landscape design is studied on. The quantitative analysis index system of highway landscape design is set up, which is made up of diversity indices, spatial indices, sensitivity indices. The method of determining these indices is analyzed. In sensitivity indices, landscape sensitivity index and visual acuity index are set up based on the dynamic and static characters of highway landscape.

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22

Haraldsdottir, A., P. T. Kabamba, and A. G. Ulsoy. "Sensitivity Reduction by State Derivative Feedback." Journal of Dynamic Systems, Measurement, and Control 110, no. 1 (March 1, 1988): 84–93. http://dx.doi.org/10.1115/1.3152655.

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This paper shows that the sensitivity of state feedback control systems can be reduced by additional state derivative feedback, for a fixed closed loop eigenstructure. The price of this sensitivity reduction is in general noise response amplification. Two indices which quantify stability robustness and response sensitivity are given for time invariant continuous time and discrete time systems, together with an index of response to disturbances and noise. Closed form expressions for the gradients of these indices are given. A two step design procedure is proposed which consists of first selecting a closed loop eigenstructure, then minimizing one of the sensitivity indices under a magnitude constraint on the noise response. Examples are given to illustrate this original design procedure.

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23

Sobol’, I. M., and S. Kucherenko. "Derivative based global sensitivity measures and their link with global sensitivity indices." Mathematics and Computers in Simulation 79, no. 10 (June 2009): 3009–17. http://dx.doi.org/10.1016/j.matcom.2009.01.023.

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24

Weirs, V. Gregory, Laura P. Swiler, William J. Rider, Brian M. Adams, James R. Kamm, and Michael S. Eldred. "Sensitivity analysis using stochastic expansion methods to calculate variance-based sensitivity indices." Procedia - Social and Behavioral Sciences 2, no. 6 (2010): 7765–67. http://dx.doi.org/10.1016/j.sbspro.2010.05.218.

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25

Fraiman, R., F. Gamboa, and Leonardo Moreno. "SENSITIVITY INDICES FOR OUTPUT ON A RIEMANNIAN MANIFOLD." International Journal for Uncertainty Quantification 10, no. 4 (2020): 297–314. http://dx.doi.org/10.1615/int.j.uncertaintyquantification.2020029614.

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26

Bilyk, Victoriia, Olena Kolomytseva, Olha Myshkovych, Nataliia Tymoshyk, and Denis Shcherbatykh. "Modeling sensitivity indices of industrial enterprise organizational change." Revista Amazonia Investiga 10, no. 45 (October 29, 2021): 230–41. http://dx.doi.org/10.34069/ai/2021.45.09.23.

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Evaluation of sensitivity of commercial enterprises to organizational changes should be made in terms of short-term planning for which it is important to ensure the financial results, as well as in terms of long-term planning, which is important for non-monetary indicators of development effectiveness. To solve this problem, the paper is designed model sensitivity Descriptive indicators of industrial enterprises to organizational changes, reflecting monetary and non-monetary effects of organizational change. The authors determined that the proposed model allows for the analysis of organizational change with regard to their impact on monetary and non-monetary efficiency. This paper contributes to the theory and practice at the border to ensure a balance between short-term and long-term development of industrial enterprises. Convincingly demonstrated the possibility of using research results in practice.

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27

Korn, A. J., C. Maraston, and D. Thomas. "The sensitivity of Lick indices to abundance variations." Astronomy & Astrophysics 438, no. 2 (July 8, 2005): 685–704. http://dx.doi.org/10.1051/0004-6361:20042126.

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28

Žarković, Miloš, Jasmina Ćirić, Biljana Beleslin, Mirjana Stojković, Slavica Savić, Miloš Stojanović, and Tijana Lalić. "Variability of HOMA and QUICKI insulin sensitivity indices." Scandinavian Journal of Clinical and Laboratory Investigation 77, no. 4 (March 31, 2017): 295–97. http://dx.doi.org/10.1080/00365513.2017.1306878.

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29

Cardou, P., S. Bouchard, and C. Gosselin. "Kinematic-Sensitivity Indices for Dimensionally Nonhomogeneous Jacobian Matrices." IEEE Transactions on Robotics 26, no. 1 (February 2010): 166–73. http://dx.doi.org/10.1109/tro.2009.2037252.

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30

Dimov, I., and R. Georgieva. "Monte Carlo algorithms for evaluating Sobol’ sensitivity indices." Mathematics and Computers in Simulation 81, no. 3 (November 2010): 506–14. http://dx.doi.org/10.1016/j.matcom.2009.09.005.

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31

D. F. Wanjura and J. L. Hatfield. "Sensitivity of Spectral Vegetative Indices to Crop Biomass." Transactions of the ASAE 30, no. 3 (1987): 0810–16. http://dx.doi.org/10.13031/2013.30479.

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32

Maeda, Naoyuki, Shigeru Sato, Hitoshi Watanabe, Yoshitsugu Inoue, Takashi Fujikado, Yoshikazu Shimomura, and Yasuo Tano. "Prediction of letter contrast sensitivity using videokeratographic indices." American Journal of Ophthalmology 129, no. 6 (June 2000): 759–63. http://dx.doi.org/10.1016/s0002-9394(00)00380-9.

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33

Hall, Jim W. "Uncertainty-based sensitivity indices for imprecise probability distributions." Reliability Engineering & System Safety 91, no. 10-11 (October 2006): 1443–51. http://dx.doi.org/10.1016/j.ress.2005.11.042.

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34

Wei, Pengfei, Zhenzhou Lu, and Jingwen Song. "Regional and parametric sensitivity analysis of Sobol׳ indices." Reliability Engineering & System Safety 137 (May 2015): 87–100. http://dx.doi.org/10.1016/j.ress.2014.12.012.

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35

Furtula, Boris, Ivan Gutman, and Matthias Dehmer. "On structure-sensitivity of degree-based topological indices." Applied Mathematics and Computation 219, no. 17 (May 2013): 8973–78. http://dx.doi.org/10.1016/j.amc.2013.03.072.

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36

Yun, Wanying, Zhenzhou Lu, Xian Jiang, and Shiyu Liu. "An efficient method for estimating global sensitivity indices." International Journal for Numerical Methods in Engineering 108, no. 11 (May 27, 2016): 1275–89. http://dx.doi.org/10.1002/nme.5249.

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37

Sobol, I. M., and S. S. Kucherenko. "Global sensitivity indices for nonlinear mathematical models. Review." Wilmott 2005, no. 1 (January 2005): 56–61. http://dx.doi.org/10.1002/wilm.42820050114.

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38

Bauch, Christopher D., Wayne O. Olsen, and Angela F. Pool. "ABR Indices." American Journal of Audiology 5, no. 1 (March 1996): 97–104. http://dx.doi.org/10.1044/1059-0889.0501.97.

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ABR absolute latencies and interpeak intervals were reviewed for 684 non-tumor ears and 75 eighth-nerve tumor ears having various degrees of high frequency hearing loss. For non-tumor ears, the percentage of abnormal absolute latencies for waves I, III, and V increased rather systematically as hearing loss increased, whereas absolute latencies for eighth-nerve tumor ears were largely abnormal regardless of hearing loss. Interpeak intervals were normal for most of the non-tumor ears, but the I–III and I–V intervals were abnormal for most of the tumor ears. The most sensitive index for otoneurologic assessment was a combination of abnormal wave V interaural latency differences or I–V interpeak interval, and the most specific criterion was the I–V interpeak interval. Tumor size influenced sensitivity of most ABR indices.

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39

Li, Ya Li, and Min Zhou. "Sensitivity Analysis of Rockfall Kinematic Parameters in Expressway." Advanced Materials Research 243-249 (May 2011): 3263–67. http://dx.doi.org/10.4028/www.scientific.net/amr.243-249.3263.

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The rockfall trajectories are affected by many kinematic parameters. So it is very necessary to exactly analyze the sensitivity of rockfall kinematic parameters to the control indices for design of protective structures. In this paper, the kinematics combined with the orthogonal test is adopted to analyze the sensitivity of rockfall kinematic parameters. Taking the rockfall hazard near the DK27+120 section of the jing-ying expressway in china for example, three control indices are taken as the testing indices, and five kinematic parameters are taken as the testing factors. The orthogonal test table is used to design twenty-five kinds of schemes, and the numerical simulation tests of rockfall trajectories are carried out. The range analysis are performed to study the sensitivity of rockfall kinematic parameters, and then the main parameters influencing the control indices for design of protective structures are obtained, which provides scientific basis for the rockfall prevention in jing-ying expressway.

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40

Yue, Jianpeng, Jaime A. Camelio, Melida Chin, and Wayne Cai. "Product-Oriented Sensitivity Analysis for Multistation Compliant Assemblies." Journal of Mechanical Design 129, no. 8 (July 25, 2006): 844–51. http://dx.doi.org/10.1115/1.2735341.

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Dimensional variation in assembled products directly affects product performance. To reduce dimensional variation, it is necessary that an assembly be robust. A robust assembly is less sensitive to input variation from the product and process components, such as incoming parts, subassemblies, fixtures, and welding guns. In order to effectively understand the sensitivity of an assembly to input variation, an appropriate set of metrics must be defined. In this paper, three product-oriented indices, including pattern sensitivity index, component sensitivity index, and station sensitivity index, are defined. These indices can be utilized to measure the variation influence of a pattern, an individual part, and/or component, and components at a particular station to the dimensional quality of a final assembly. Additionally, the relationships among these sensitivity indices are established. Based on these relationships, the ranges of the sensitivity indices are derived. Finally, a case study of a sheet metal assembly is presented and discussed to illustrate the applicability of these metrics.

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41

Kala, Zdeněk. "New Importance Measures Based on Failure Probability in Global Sensitivity Analysis of Reliability." Mathematics 9, no. 19 (September 29, 2021): 2425. http://dx.doi.org/10.3390/math9192425.

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This article presents new sensitivity measures in reliability-oriented global sensitivity analysis. The obtained results show that the contrast and the newly proposed sensitivity measures (entropy and two others) effectively describe the influence of input random variables on the probability of failure Pf. The contrast sensitivity measure builds on Sobol, using the variance of the binary outcome as either a success (0) or a failure (1). In Bernoulli distribution, variance Pf(1 − Pf) and discrete entropy—Pfln(Pf) − (1 − Pf)ln(1 − Pf) are similar to dome functions. By replacing the variance with discrete entropy, a new alternative sensitivity measure is obtained, and then two additional new alternative measures are derived. It is shown that the desired property of all the measures is a dome shape; the rise is not important. Although the decomposition of sensitivity indices with alternative measures is not proven, the case studies suggest a rationale structure of all the indices in the sensitivity analysis of small Pf. The sensitivity ranking of input variables based on the total indices is approximately the same, but the proportions of the first-order and the higher-order indices are very different. Discrete entropy gives significantly higher proportions of first-order sensitivity indices than the other sensitivity measures, presenting entropy as an interesting new sensitivity measure of engineering reliability.

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42

Srivastava, Ankur, Arun K. Subramaniyan, and Liping Wang. "Analytical global sensitivity analysis with Gaussian processes." Artificial Intelligence for Engineering Design, Analysis and Manufacturing 31, no. 3 (August 2017): 235–50. http://dx.doi.org/10.1017/s0890060417000142.

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AbstractMethods for efficient variance-based global sensitivity analysis of complex high-dimensional problems are presented and compared. Variance decomposition methods rank inputs according to Sobol indices that can be computationally expensive to evaluate. Main and interaction effect Sobol indices can be computed analytically in the Kennedy and O'Hagan framework with Gaussian processes. These methods use the high-dimensional model representation concept for variance decomposition that presents a unique model representation when inputs are uncorrelated. However, when the inputs are correlated, multiple model representations may be possible leading to ambiguous sensitivity ranking with Sobol indices. In this work, we present the effect of input correlation on sensitivity analysis and discuss the methods presented by Li and Rabitz in the context of Kennedy and O'Hagan's framework with Gaussian processes. Results are demonstrated on simulated and real problems for correlated and uncorrelated inputs and demonstrate the utility of variance decomposition methods for sensitivity analysis.

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43

Modzelewska, Aneta, Krzysztof Stereńczak, Monika Mierczyk, Sylwia Maciuk, Radomir Bałazy, and Tomasz Zawiła-Niedźwiecki. "Sensitivity of vegetation indices in relation to parameters of Norway spruce stands." Folia Forestalia Polonica 59, no. 2 (June 27, 2017): 85–98. http://dx.doi.org/10.1515/ffp-2017-0009.

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AbstractThe main goal of this research is to shed further light on the sensitivity of the vegetation indices to spatial changes of stand parameters. The analysis was done within mountain forests in the Sudetes and the Beskids in southern Poland. Some 1327 stands were analysed with more than 70 percent of spruce contribution in the species composition. The response of selected vegetation indices was verified in relation to the alterations of spruce participation, stand height, volume, stand density and diameter. The following indices were analysed: Normalized Difference Vegetation Index, Normalized Difference Red Edge Index, Green Normalized Difference Vegetation Index and Wide Dynamic Range Vegetation Index. Indices were calculated based on the Rapid Eye (Black Bridge) images. All the analysed stand characteristics influence the values of vegetation indices. In general: mean height, diameter at breast height, volume and spruce participation are the most negatively correlated with the indices. Density is a variable that, in general, cannot directly be used for indices correction, because it is hard to find any stable trend. NDRE is the most stable index for the analysis of stand characteristics.

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44

Makinde, Akeem. "Sensitivity of Okra Growth Indices to Various Moisture Conditions." American Journal of Agricultural and Biological Sciences 17, no. 1 (January 1, 2022): 51–57. http://dx.doi.org/10.3844/ajabssp.2022.51.57.

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45

Chrenova, Jana, Zuzana Rausova, Adela Penesova, and Ladislav Dedik. "Comparison of insulin sensitivity indices properties calculated from OGTT." Open Medicine 6, no. 5 (October 1, 2011): 567–74. http://dx.doi.org/10.2478/s11536-011-0056-7.

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AbstractThe aim of this study was to present the properties of insulin sensitivity indices formulas to justify selection of formulas to evaluate of insulin sensitivity for calculation from an oral glucose tolerance test (OGTT) data. Twelve of the most applicable formulae for ISI calculation were analyzed in the view of two sets of results: 1) point contrasts, calculated as the ratio of average ISI values in lean and obese groups of patients; and 2) interval contrasts, calculated as ratios of T from the two-sided t-test, evaluated as dimensionless, mutually comparable contrasts within a continuous scale. Statistical significance of individual ISIs in terms of their contrasts was evaluated by two-sided t-tests. P<0.001 was a considered statistically significance between a group of 59 healthy volunteers with BMI<25 kg/m2 and a group of 63 volunteers with BMI≥25 kg/m2 who underwent frequent OGTT sampling. To compare data of an individual subject with the standard, we recommend selecting the formulas with a high point contrast. To compare of data of several subject groups, we recommend using the formulas with a high interval contrast.

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46

Chastaing, G., F. Gamboa, and C. Prieur. "Generalized Sobol sensitivity indices for dependent variables: numerical methods." Journal of Statistical Computation and Simulation 85, no. 7 (September 25, 2014): 1306–33. http://dx.doi.org/10.1080/00949655.2014.960415.

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47

Kucherenko, S., and S. Song. "Different numerical estimators for main effect global sensitivity indices." Reliability Engineering & System Safety 165 (September 2017): 222–38. http://dx.doi.org/10.1016/j.ress.2017.04.003.

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48

Bokov, Pavel M. "Asymptotic Analysis for the Variance-Based Global Sensitivity Indices." Science and Technology of Nuclear Installations 2012 (2012): 1–8. http://dx.doi.org/10.1155/2012/253045.

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We discuss the estimation of the uncertainty and sensitivity parameters for a model response under the assumption that the input variables are normally distributed and block-wise correlated with the covariance matrix, which is small in some norm. These conditions may arise when considering the impact of the group-wise neutron cross-sections' uncertainties on the uncertainty of some reactor parameters such as the neutron multiplication factor. The variance-based global sensitivity analysis, considered in our work, involves the calculation of multidimensional integrals. When the input uncertainties are small, the values of these integrals can be estimated using an asymptotic analysis method called the Laplace approximation. The asymptotic formulas for the output variance and for the global sensitivity indices have been obtained using the Laplace approximation method. It is demonstrated that the asymptotic formula for uncertainty propagation matches the uncertainty propagation formula being used in the local sensitivity analysis. The applicability of the obtained asymptotic approximations was successfully demonstrated on a test problem with realistic cross-section and covariance matrix values.

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49

Mannucci, E., G. Bardini, F. Rotella, and C. M. Rotella. "Comparison among different insulin sensitivity indices in obese patients." Diabetic Medicine 20, no. 6 (June 2003): 462–66. http://dx.doi.org/10.1046/j.1464-5491.2003.00935.x.

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50

Tank, J., R. M. Baevski, A. Fender, A. R. Baevski, K. F. Graves, K. Ploewka, and M. Weck. "Reference values of indices of spontaneous baroreceptor reflex sensitivity." American Journal of Hypertension 13, no. 3 (March 1, 2000): 268–75. http://dx.doi.org/10.1016/s0895-7061(99)00172-7.

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