IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v56y2010i6p997-1011.html
   My bibliography  Save this article

Assessing Joint Distributions with Isoprobability Contours

Author

Listed:
  • Ali E. Abbas

    (Department of Industrial and Enterprise Systems Engineering, College of Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801)

  • David V. Budescu

    (Department of Psychology, Fordham University, Bronx, New York 10458; and Department of Psychology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801)

  • Yuhong (Rola) Gu

    (Department of Psychology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801)

Abstract

We present a new method for constructing joint probability distributions of continuous random variables using isoprobability contours--sets of points with the same joint cumulative probability. This approach reduces the joint probability assessment into a one-dimensional cumulative probability assessment using a sequence of binary choices between various combinations of the variables of interest. The approach eliminates the need to assess directly the dependence, or association, between the variables. We discuss properties of isoprobability contours and methods for their assessment in practice. We also report results of a study in which subjects assessed the 50th percentile isoprobability contour of the joint distribution of weight and height. We use the data to show how to use the assessed contours to construct the joint distribution and to infer (indirectly) the dependence between the variables.

Suggested Citation

  • Ali E. Abbas & David V. Budescu & Yuhong (Rola) Gu, 2010. "Assessing Joint Distributions with Isoprobability Contours," Management Science, INFORMS, vol. 56(6), pages 997-1011, June.
    • Handle: RePEc:inm:ormnsc:v:56:y:2010:i:6:p:997-1011
    DOI: 10.1287/mnsc.1100.1161
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.1100.1161
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.1100.1161?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
    ---><---

    References listed on IDEAS

    as
    1. Woojune Yi & Vicki M. Bier, 1998. "An Application of Copulas to Accident Precursor Analysis," Management Science, INFORMS, vol. 44(12-Part-2), pages 257-270, December.
    2. K. R. MacCrimmon & M. Toda, 1969. "The Experimental Determination of Indifference Curves," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(4), pages 433-451.
    3. Thomas S. Wallsten & David V. Budescu, 1983. "State of the Art---Encoding Subjective Probabilities: A Psychological and Psychometric Review," Management Science, INFORMS, vol. 29(2), pages 151-173, February.
    4. Robert T. Clemen & Terence Reilly, 1999. "Correlations and Copulas for Decision and Risk Analysis," Management Science, INFORMS, vol. 45(2), pages 208-224, February.
    5. Robert T. Clemen & Gregory W. Fischer & Robert L. Winkler, 2000. "Assessing Dependence: Some Experimental Results," Management Science, INFORMS, vol. 46(8), pages 1100-1115, August.
    6. Ali E. Abbas & David V. Budescu & Hsiu-Ting Yu & Ryan Haggerty, 2008. "A Comparison of Two Probability Encoding Methods: Fixed Probability vs. Fixed Variable Values," Decision Analysis, INFORMS, vol. 5(4), pages 190-202, December.
    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. David Kaplan & Jianshen Chen, 2012. "A Two-Step Bayesian Approach for Propensity Score Analysis: Simulations and Case Study," Psychometrika, Springer;The Psychometric Society, vol. 77(3), pages 581-609, July.
    2. Tim Bedford & Alireza Daneshkhah & Kevin J. Wilson, 2016. "Approximate Uncertainty Modeling in Risk Analysis with Vine Copulas," Risk Analysis, John Wiley & Sons, vol. 36(4), pages 792-815, April.
    3. Xiaochun Meng & James W. Taylor & Souhaib Ben Taieb & Siran Li, 2020. "Scores for Multivariate Distributions and Level Sets," Papers 2002.09578, arXiv.org, revised Jun 2023.
    4. Werner, Christoph & Bedford, Tim & Cooke, Roger M. & Hanea, Anca M. & Morales-Nápoles, Oswaldo, 2017. "Expert judgement for dependence in probabilistic modelling: A systematic literature review and future research directions," European Journal of Operational Research, Elsevier, vol. 258(3), pages 801-819.
    5. Lockwood, Matthew, 2016. "The UK's Levy Control Framework for renewable electricity support: Effects and significance," Energy Policy, Elsevier, vol. 97(C), pages 193-201.

    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. Donald L. Keefer & Craig W. Kirkwood & James L. Corner, 2004. "Perspective on Decision Analysis Applications, 1990–2001," Decision Analysis, INFORMS, vol. 1(1), pages 4-22, March.
    2. Tianyang Wang & James S. Dyer, 2012. "A Copulas-Based Approach to Modeling Dependence in Decision Trees," Operations Research, INFORMS, vol. 60(1), pages 225-242, February.
    3. J. Eric Bickel & James E. Smith, 2006. "Optimal Sequential Exploration: A Binary Learning Model," Decision Analysis, INFORMS, vol. 3(1), pages 16-32, March.
    4. Tianyang Wang & James S. Dyer & Warren J. Hahn, 2017. "Sensitivity analysis of decision making under dependent uncertainties using copulas," EURO Journal on Decision Processes, Springer;EURO - The Association of European Operational Research Societies, vol. 5(1), pages 117-139, November.
    5. Wang, Fan & Li, Heng & Dong, Chao & Ding, Lieyun, 2019. "Knowledge representation using non-parametric Bayesian networks for tunneling risk analysis," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    6. Yuyu Fan & David V. Budescu & David Mandel & Mark Himmelstein, 2019. "Improving Accuracy by Coherence Weighting of Direct and Ratio Probability Judgments," Decision Analysis, INFORMS, vol. 16(3), pages 197-217, September.
    7. Saemi Park & David V. Budescu, 2015. "Aggregating multiple probability intervals to improve calibration," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 10(2), pages 130-143, March.
    8. repec:cup:judgdm:v:10:y:2015:i:2:p:130-143 is not listed on IDEAS
    9. Gillian Anderson & Lesley Walls & Matthew Revie & Euan Fenelon & Calum Storie, 2015. "Quantifying intra-organisational risks: An analysis of practice-theory tensions in probability elicitation to improve technical risk management in an energy utility," Journal of Risk and Reliability, , vol. 229(3), pages 171-180, June.
    10. Khakzad, Nima & Khan, Faisal & Paltrinieri, Nicola, 2014. "On the application of near accident data to risk analysis of major accidents," Reliability Engineering and System Safety, Elsevier, vol. 126(C), pages 116-125.
    11. James K. Hammitt & Yifan Zhang, 2013. "Combining Experts’ Judgments: Comparison of Algorithmic Methods Using Synthetic Data," Risk Analysis, John Wiley & Sons, vol. 33(1), pages 109-120, January.
    12. Meade, Nigel & Islam, Towhidul, 2010. "Using copulas to model repeat purchase behaviour - An exploratory analysis via a case study," European Journal of Operational Research, Elsevier, vol. 200(3), pages 908-917, February.
    13. Jesus Palomo & David Rios Insua & Fabrizio Ruggeri, 2007. "Modeling External Risks in Project Management," Risk Analysis, John Wiley & Sons, vol. 27(4), pages 961-978, August.
    14. van Dorp, J. Rene, 2005. "Statistical dependence through common risk factors: With applications in uncertainty analysis," European Journal of Operational Research, Elsevier, vol. 161(1), pages 240-255, February.
    15. Ali E. Abbas, 2009. "Multiattribute Utility Copulas," Operations Research, INFORMS, vol. 57(6), pages 1367-1383, December.
    16. Robin L. Dillon & Richard John & Detlof von Winterfeldt, 2002. "Assessment of Cost Uncertainties for Large Technology Projects: A Methodology and an Application," Interfaces, INFORMS, vol. 32(4), pages 52-66, August.
    17. Werner, Christoph & Bedford, Tim & Cooke, Roger M. & Hanea, Anca M. & Morales-Nápoles, Oswaldo, 2017. "Expert judgement for dependence in probabilistic modelling: A systematic literature review and future research directions," European Journal of Operational Research, Elsevier, vol. 258(3), pages 801-819.
    18. Huifen Chen, 2001. "Initialization for NORTA: Generation of Random Vectors with Specified Marginals and Correlations," INFORMS Journal on Computing, INFORMS, vol. 13(4), pages 312-331, November.
    19. Tianyang Wang & James S. Dyer & John C. Butler, 2016. "Modeling Correlated Discrete Uncertainties in Event Trees with Copulas," Risk Analysis, John Wiley & Sons, vol. 36(2), pages 396-410, February.
    20. Morales, O. & Kurowicka, D. & Roelen, A., 2008. "Eliciting conditional and unconditional rank correlations from conditional probabilities," Reliability Engineering and System Safety, Elsevier, vol. 93(5), pages 699-710.
    21. Wagner, Stephan M. & Bode, Christoph & Koziol, Philipp, 2009. "Supplier default dependencies: Empirical evidence from the automotive industry," European Journal of Operational Research, Elsevier, vol. 199(1), pages 150-161, November.

    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:inm:ormnsc:v:56:y:2010:i:6:p:997-1011. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.