IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v91y2006i8p861-871.html
   My bibliography  Save this article

Validation of models with multivariate output

Author

Listed:
  • Rebba, Ramesh
  • Mahadevan, Sankaran

Abstract

This paper develops metrics for validating computational models with experimental data, considering uncertainties in both. A computational model may generate multiple response quantities and the validation experiment might yield corresponding measured values. Alternatively, a single response quantity may be predicted and observed at different spatial and temporal points. Model validation in such cases involves comparison of multiple correlated quantities. Multiple univariate comparisons may give conflicting inferences. Therefore, aggregate validation metrics are developed in this paper. Both classical and Bayesian hypothesis testing are investigated for this purpose, using multivariate analysis. Since, commonly used statistical significance tests are based on normality assumptions, appropriate transformations are investigated in the case of non-normal data. The methodology is implemented to validate an empirical model for energy dissipation in lap joints under dynamic loading.

Suggested Citation

  • Rebba, Ramesh & Mahadevan, Sankaran, 2006. "Validation of models with multivariate output," Reliability Engineering and System Safety, Elsevier, vol. 91(8), pages 861-871.
  • Handle: RePEc:eee:reensy:v:91:y:2006:i:8:p:861-871
    DOI: 10.1016/j.ress.2005.09.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832005001870
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.ress.2005.09.004?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. Srivastava, M. S. & Hui, T. K., 1987. "On assessing multivariate normality based on shapiro-wilk W statistic," Statistics & Probability Letters, Elsevier, vol. 5(1), pages 15-18, January.
    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. Ling, You & Mahadevan, Sankaran, 2013. "Quantitative model validation techniques: New insights," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 217-231.
    2. Li, Luyi & Lu, Zhenzhou, 2018. "A new method for model validation with multivariate output," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 579-592.
    3. Ming-Na Tong & Fu-Qiang Shen & Chen-Xing Cui, 2022. "The Inverse Transformation of L-Hermite Model and Its Application in Structural Reliability Analysis," Mathematics, MDPI, vol. 10(22), pages 1-15, November.
    4. Teferra, Kirubel & Shields, Michael D. & Hapij, Adam & Daddazio, Raymond P., 2014. "Mapping model validation metrics to subject matter expert scores for model adequacy assessment," Reliability Engineering and System Safety, Elsevier, vol. 132(C), pages 9-19.
    5. Ao, Dan & Hu, Zhen & Mahadevan, Sankaran, 2017. "Design of validation experiments for life prediction models," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 22-33.
    6. Zhao, Lufeng & Lu, Zhenzhou & Yun, Wanying & Wang, Wenjin, 2017. "Validation metric based on Mahalanobis distance for models with multiple correlated responses," Reliability Engineering and System Safety, Elsevier, vol. 159(C), pages 80-89.
    7. Li, Wei & Chen, Wei & Jiang, Zhen & Lu, Zhenzhou & Liu, Yu, 2014. "New validation metrics for models with multiple correlated responses," Reliability Engineering and System Safety, Elsevier, vol. 127(C), pages 1-11.
    8. Mullins, Joshua & Ling, You & Mahadevan, Sankaran & Sun, Lin & Strachan, Alejandro, 2016. "Separation of aleatory and epistemic uncertainty in probabilistic model validation," Reliability Engineering and System Safety, Elsevier, vol. 147(C), pages 49-59.
    9. Jiang, Xiaomo & Yuan, Yong & Liu, Xian, 2013. "Bayesian inference method for stochastic damage accumulation modeling," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 126-138.

    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. Diego Norena-Chavez & Ruben Guevara, 2020. "Entrepreneurial Passion and Self-Efficacy as Factors Explaining Innovative Behavior: A Mediation Model," International Journal of Economics & Business Administration (IJEBA), International Journal of Economics & Business Administration (IJEBA), vol. 0(3), pages 352-373.
    2. Sándor Csörgő, 1989. "Consistency of some tests for multivariate normality," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 36(1), pages 107-116, December.
    3. Jurgen A. Doornik & Henrik Hansen, 2008. "An Omnibus Test for Univariate and Multivariate Normality," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(s1), pages 927-939, December.
    4. Liang, Jiajuan & Tang, Man-Lai & Chan, Ping Shing, 2009. "A generalized Shapiro-Wilk W statistic for testing high-dimensional normality," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3883-3891, September.
    5. Bruno Ebner & Norbert Henze, 2020. "Tests for multivariate normality—a critical review with emphasis on weighted $$L^2$$ L 2 -statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 845-892, December.
    6. Kim, Namhyun, 2016. "A robustified Jarque–Bera test for multivariate normality," Economics Letters, Elsevier, vol. 140(C), pages 48-52.

    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:91:y:2006:i:8:p:861-871. 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.