IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v93y2008i7p1047-1059.html
   My bibliography  Save this article

Extension of Latin hypercube samples with correlated variables

Author

Listed:
  • Sallaberry, C.J.
  • Helton, J.C.
  • Hora, S.C.

Abstract

A procedure for extending the size of a Latin hypercube sample (LHS) with rank correlated variables is described and illustrated. The extension procedure starts with an LHS of size m and associated rank correlation matrix C and constructs a new LHS of size 2m that contains the elements of the original LHS and has a rank correlation matrix that is close to the original rank correlation matrix C. The procedure is intended for use in conjunction with uncertainty and sensitivity analysis of computationally demanding models in which it is important to make efficient use of a necessarily limited number of model evaluations.

Suggested Citation

  • Sallaberry, C.J. & Helton, J.C. & Hora, S.C., 2008. "Extension of Latin hypercube samples with correlated variables," Reliability Engineering and System Safety, Elsevier, vol. 93(7), pages 1047-1059.
    • Handle: RePEc:eee:reensy:v:93:y:2008:i:7:p:1047-1059
    DOI: 10.1016/j.ress.2007.04.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832007001378
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2007.04.005?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kleijnen, Jack P.C., 1992. "Sensitivity analysis of simulation experiments: regression analysis and statistical design," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 34(3), pages 297-315.
    2. Helton, J.C. & Johnson, J.D. & Sallaberry, C.J. & Storlie, C.B., 2006. "Survey of sampling-based methods for uncertainty and sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 91(10), pages 1175-1209.
    3. Tong, Charles, 2006. "Refinement strategies for stratified sampling methods," Reliability Engineering and System Safety, Elsevier, vol. 91(10), pages 1257-1265.
    4. Garthwaite, Paul H. & Kadane, Joseph B. & O'Hagan, Anthony, 2005. "Statistical Methods for Eliciting Probability Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 680-701, June.
    5. Kleijnen, J.P.C., 1997. "Sensitivity analysis and related analyses : A review of some statistical techniques," Other publications TiSEM 7969b135-47c5-4d76-9241-c, Tilburg University, School of Economics and Management.
    6. Saltelli, A. & Andres, T. H. & Homma, T., 1993. "Sensitivity analysis of model output : An investigation of new techniques," Computational Statistics & Data Analysis, Elsevier, vol. 15(2), pages 211-238, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hou, Tianfeng & Nuyens, Dirk & Roels, Staf & Janssen, Hans, 2019. "Quasi-Monte Carlo based uncertainty analysis: Sampling efficiency and error estimation in engineering applications," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    2. Vikram V. Garg & Roy H. Stogner, 2017. "Hierarchical Latin Hypercube Sampling," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 673-682, April.
    3. Ju, Shin-Jon, 2009. "On the distribution type of uncertain inputs for probabilistic assessment," Reliability Engineering and System Safety, Elsevier, vol. 94(5), pages 964-968.
    4. Jin Xu & Jiajie Chen & Peter Z. G. Qian, 2015. "Sequentially Refined Latin Hypercube Designs: Reusing Every Point," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1696-1706, December.
    5. Shields, Michael D. & Teferra, Kirubel & Hapij, Adam & Daddazio, Raymond P., 2015. "Refined Stratified Sampling for efficient Monte Carlo based uncertainty quantification," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 310-325.
    6. Blatman, Géraud & Sudret, Bruno, 2010. "Efficient computation of global sensitivity indices using sparse polynomial chaos expansions," Reliability Engineering and System Safety, Elsevier, vol. 95(11), pages 1216-1229.
    7. Janssen, Hans, 2013. "Monte-Carlo based uncertainty analysis: Sampling efficiency and sampling convergence," Reliability Engineering and System Safety, Elsevier, vol. 109(C), pages 123-132.
    8. Sui Peng & Huixiang Chen & Yong Lin & Tong Shu & Xingyu Lin & Junjie Tang & Wenyuan Li & Weijie Wu, 2019. "Probabilistic Power Flow for Hybrid AC/DC Grids with Ninth-Order Polynomial Normal Transformation and Inherited Latin Hypercube Sampling," Energies, MDPI, vol. 12(16), pages 1-21, August.
    9. Bui, Ha & Sakurahara, Tatsuya & Pence, Justin & Reihani, Seyed & Kee, Ernie & Mohaghegh, Zahra, 2019. "An algorithm for enhancing spatiotemporal resolution of probabilistic risk assessment to address emergent safety concerns in nuclear power plants," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 405-428.
    10. Yongkai An & Wenxi Lu & Weiguo Cheng, 2015. "Surrogate Model Application to the Identification of Optimal Groundwater Exploitation Scheme Based on Regression Kriging Method—A Case Study of Western Jilin Province," IJERPH, MDPI, vol. 12(8), pages 1-22, July.
    11. Zio, E. & Pedroni, N., 2009. "Functional failure analysis of a thermal–hydraulic passive system by means of Line Sampling," Reliability Engineering and System Safety, Elsevier, vol. 94(11), pages 1764-1781.
    12. Francesco Di Maio & Nicola Pedroni & Barnabás Tóth & Luciano Burgazzi & Enrico Zio, 2021. "Reliability Assessment of Passive Safety Systems for Nuclear Energy Applications: State-of-the-Art and Open Issues," Energies, MDPI, vol. 14(15), pages 1-17, August.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Helton, Jon C., 2011. "Quantification of margins and uncertainties: Conceptual and computational basis," Reliability Engineering and System Safety, Elsevier, vol. 96(9), pages 976-1013.
    2. Storlie, Curtis B. & Helton, Jon C., 2008. "Multiple predictor smoothing methods for sensitivity analysis: Description of techniques," Reliability Engineering and System Safety, Elsevier, vol. 93(1), pages 28-54.
    3. Helton, Jon C. & Hansen, Clifford W. & Sallaberry, Cédric J., 2012. "Uncertainty and sensitivity analysis in performance assessment for the proposed high-level radioactive waste repository at Yucca Mountain, Nevada," Reliability Engineering and System Safety, Elsevier, vol. 107(C), pages 44-63.
    4. Helton, J.C. & Johnson, J.D. & Sallaberry, C.J. & Storlie, C.B., 2006. "Survey of sampling-based methods for uncertainty and sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 91(10), pages 1175-1209.
    5. Chen, Xin & Molina-Cristóbal, Arturo & Guenov, Marin D. & Riaz, Atif, 2019. "Efficient method for variance-based sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 181(C), pages 97-115.
    6. Helton, Jon C. & Brooks, Dusty M. & Sallaberry, Cédric J., 2020. "Margins associated with loss of assured safety for systems with multiple weak links and strong links," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    7. Marrel, Amandine & Iooss, Bertrand & Van Dorpe, François & Volkova, Elena, 2008. "An efficient methodology for modeling complex computer codes with Gaussian processes," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4731-4744, June.
    8. Marrel, Amandine & Iooss, Bertrand & Laurent, Béatrice & Roustant, Olivier, 2009. "Calculations of Sobol indices for the Gaussian process metamodel," Reliability Engineering and System Safety, Elsevier, vol. 94(3), pages 742-751.
    9. Blatman, Géraud & Sudret, Bruno, 2010. "Efficient computation of global sensitivity indices using sparse polynomial chaos expansions," Reliability Engineering and System Safety, Elsevier, vol. 95(11), pages 1216-1229.
    10. Wu, Di & Zhang, Taoyuan & Zhang, Jiqiang & Lv, Hongyi & Yue, Chao & Fu, Mengze, 2024. "Sensitivity analysis and multiobjective optimization for rural house retrofitting considering construction and occupant behavior uncertainty: A case study of Jiaxian, China," Applied Energy, Elsevier, vol. 360(C).
    11. Maarten Ijzerman & Lotte Steuten, 2011. "Early assessment of medical technologies to inform product development and market access," Applied Health Economics and Health Policy, Springer, vol. 9(5), pages 331-347, September.
    12. Zhou, Yuekuan & Zheng, Siqian, 2020. "Uncertainty study on thermal and energy performances of a deterministic parameters based optimal aerogel glazing system using machine-learning method," Energy, Elsevier, vol. 193(C).
    13. Helton, Jon C. & Johnson, Jay D. & Sallaberry, Cédric J., 2011. "Quantification of margins and uncertainties: Example analyses from reactor safety and radioactive waste disposal involving the separation of aleatory and epistemic uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 96(9), pages 1014-1033.
    14. Plischke, Elmar & Borgonovo, Emanuele, 2019. "Copula theory and probabilistic sensitivity analysis: Is there a connection?," European Journal of Operational Research, Elsevier, vol. 277(3), pages 1046-1059.
    15. Claire Copeland & Britta Turner & Gareth Powells & Kevin Wilson, 2022. "In Search of Complementarity: Insights from an Exercise in Quantifying Qualitative Energy Futures," Energies, MDPI, vol. 15(15), pages 1-21, July.
    16. Robert Stewart & Marie Urban & Samantha Duchscherer & Jason Kaufman & April Morton & Gautam Thakur & Jesse Piburn & Jessica Moehl, 2016. "A Bayesian machine learning model for estimating building occupancy from open source data," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 81(3), pages 1929-1956, April.
    17. Garavaglia Christian & Malerba Franco & Orsenigo Luigi & Pezzoni Michele, 2014. "Innovation and Market Structure in Pharmaceuticals: An Econometric Analysis on Simulated Data," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 234(2-3), pages 274-298, April.
    18. Saurbayeva, Assemgul & Memon, Shazim Ali & Kim, Jong, 2023. "Integrated multi-stage sensitivity analysis and multi-objective optimization approach for PCM integrated residential buildings in different climate zones," Energy, Elsevier, vol. 278(PB).
    19. Donghyeon Yoo & Jinhwan Park & Jaemin Moon & Changwan Kim, 2021. "Reliability-Based Design Optimization for Reducing the Performance Failure and Maximizing the Specific Energy of Lithium-Ion Batteries Considering Manufacturing Uncertainty of Porous Electrodes," Energies, MDPI, vol. 14(19), pages 1-15, September.
    20. Nicholas M. Kiefer, 2011. "Default estimation, correlated defaults, and expert information," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(2), pages 173-192, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:reensy:v:93:y:2008:i:7:p:1047-1059. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.