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A Finite Mixture Modelling Perspective for Combining Experts’ Opinions with an Application to Quantile-Based Risk Measures

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  • Despoina Makariou

    (Department of Statistics, London School of Economics and Political Science, London WC2A 2AE, UK)

  • Pauline Barrieu

    (Department of Statistics, London School of Economics and Political Science, London WC2A 2AE, UK)

  • George Tzougas

    (Department of Statistics, London School of Economics and Political Science, London WC2A 2AE, UK)

Abstract

The key purpose of this paper is to present an alternative viewpoint for combining expert opinions based on finite mixture models. Moreover, we consider that the components of the mixture are not necessarily assumed to be from the same parametric family. This approach can enable the agent to make informed decisions about the uncertain quantity of interest in a flexible manner that accounts for multiple sources of heterogeneity involved in the opinions expressed by the experts in terms of the parametric family, the parameters of each component density, and also the mixing weights. Finally, the proposed models are employed for numerically computing quantile-based risk measures in a collective decision-making context.

Suggested Citation

  • Despoina Makariou & Pauline Barrieu & George Tzougas, 2021. "A Finite Mixture Modelling Perspective for Combining Experts’ Opinions with an Application to Quantile-Based Risk Measures," Risks, MDPI, vol. 9(6), pages 1-25, June.
    • Handle: RePEc:gam:jrisks:v:9:y:2021:i:6:p:115-:d:572157
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    1. Stephen C. Hora & Benjamin R. Fransen & Natasha Hawkins & Irving Susel, 2013. "Median Aggregation of Distribution Functions," Decision Analysis, INFORMS, vol. 10(4), pages 279-291, December.
    2. Tzougas, George & Vrontos, Spyridon & Frangos, Nicholas, 2014. "Optimal Bonus-Malus Systems Using Finite Mixture Models," ASTIN Bulletin, Cambridge University Press, vol. 44(2), pages 417-444, May.
    3. Allison, David B. & Gadbury, Gary L. & Heo, Moonseong & Fernandez, Jose R. & Lee, Cheol-Koo & Prolla, Tomas A. & Weindruch, Richard, 2002. "A mixture model approach for the analysis of microarray gene expression data," Computational Statistics & Data Analysis, Elsevier, vol. 39(1), pages 1-20, March.
    4. Dominik D. Lambrigger & Pavel V. Shevchenko & Mario V. Wuthrich, 2009. "The Quantification of Operational Risk using Internal Data, Relevant External Data and Expert Opinions," Papers 0904.1361, arXiv.org.
    5. JL Bamber & WP Aspinall & RM Cooke, 2016. "A commentary on “how to interpret expert judgment assessments of twenty-first century sea-level rise” by Hylke de Vries and Roderik SW van de Wal," Climatic Change, Springer, vol. 137(3), pages 321-328, August.
    6. Flandoli, F. & Giorgi, E. & Aspinall, W.P. & Neri, A., 2011. "Comparison of a new expert elicitation model with the Classical Model, equal weights and single experts, using a cross-validation technique," Reliability Engineering and System Safety, Elsevier, vol. 96(10), pages 1292-1310.
    7. Fabio Busetti, 2017. "Quantile Aggregation of Density Forecasts," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 79(4), pages 495-512, August.
    8. Colson, Abigail R. & Cooke, Roger M., 2017. "Cross validation for the classical model of structured expert judgment," Reliability Engineering and System Safety, Elsevier, vol. 163(C), pages 109-120.
    9. Antonio Punzo & Angelo Mazza & Antonello Maruotti, 2018. "Fitting insurance and economic data with outliers: a flexible approach based on finite mixtures of contaminated gamma distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(14), pages 2563-2584, October.
    10. Yiu-Fai Yung, 1997. "Finite mixtures in confirmatory factor-analysis models," Psychometrika, Springer;The Psychometric Society, vol. 62(3), pages 297-330, September.
    11. Miljkovic, Tatjana & Grün, Bettina, 2016. "Modeling loss data using mixtures of distributions," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 387-396.
    12. Blostein, Martin & Miljkovic, Tatjana, 2019. "On modeling left-truncated loss data using mixtures of distributions," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 35-46.
    13. Pauline Barrieu & Nicole El Karoui, 2005. "Inf-convolution of risk measures and optimal risk transfer," Finance and Stochastics, Springer, vol. 9(2), pages 269-298, April.
    14. Robert T. Clemen & Robert L. Winkler, 1999. "Combining Probability Distributions From Experts in Risk Analysis," Risk Analysis, John Wiley & Sons, vol. 19(2), pages 187-203, April.
    15. Clemen, Robert T., 1989. "Combining forecasts: A review and annotated bibliography," International Journal of Forecasting, Elsevier, vol. 5(4), pages 559-583.
    16. Marc Henry & Yuichi Kitamura & Bernard Salanié, 2014. "Partial identification of finite mixtures in econometric models," Quantitative Economics, Econometric Society, vol. 5, pages 123-144, March.
    17. Peiro, Amado, 1999. "Skewness in financial returns," Journal of Banking & Finance, Elsevier, vol. 23(6), pages 847-862, June.
    18. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    19. Gambacciani, Marco & Paolella, Marc S., 2017. "Robust normal mixtures for financial portfolio allocation," Econometrics and Statistics, Elsevier, vol. 3(C), pages 91-111.
    20. Barrieu, Pauline & El Karoui, Nicole, 2005. "Inf-convolution of risk measures and optimal risk transfer," LSE Research Online Documents on Economics 2829, London School of Economics and Political Science, LSE Library.
    21. Cooke, Roger M. & Goossens, Louis L.H.J., 2008. "TU Delft expert judgment data base," Reliability Engineering and System Safety, Elsevier, vol. 93(5), pages 657-674.
    22. Kenneth C. Lichtendahl & Yael Grushka-Cockayne & Robert L. Winkler, 2013. "Is It Better to Average Probabilities or Quantiles?," Management Science, INFORMS, vol. 59(7), pages 1594-1611, July.
    23. George Tzougas & Spyridon Vrontos & Nicholas Frangos, 2018. "Bonus-Malus Systems with Two-Component Mixture Models Arising from Different Parametric Families," North American Actuarial Journal, Taylor & Francis Journals, vol. 22(1), pages 55-91, January.
    24. Rufo, M.J. & Pérez, C.J. & Martín, J., 2010. "Merging experts' opinions: A Bayesian hierarchical model with mixture of prior distributions," European Journal of Operational Research, Elsevier, vol. 207(1), pages 284-289, November.
    25. Tsz Chai Fung & George Tzougas & Mario Wuthrich, 2021. "Mixture composite regression models with multi-type feature selection," Papers 2103.07200, arXiv.org, revised Jul 2021.
    26. Barrieu, Pauline & Scandolo, Giacomo, 2015. "Assessing financial model risk," European Journal of Operational Research, Elsevier, vol. 242(2), pages 546-556.
    27. Tzougas, George & Vrontos, Spyridon & Frangos, Nicholas, 2014. "Optimal Bonus-Malus Systems using finite mixture models," LSE Research Online Documents on Economics 70919, London School of Economics and Political Science, LSE Library.
    28. Pauline Barrieu & Claudia Ravanelli, 2015. "Robust Capital Requirements with Model Risk," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 44(1), pages 1-28, February.
    29. Tzougas, George & Vrontos, Spyridon & Frangos, Nicholas, 2018. "Bonus-Malus systems with two component mixture models arising from different parametric families," LSE Research Online Documents on Economics 84301, London School of Economics and Political Science, LSE Library.
    30. Fung, Tsz Chai & Badescu, Andrei L. & Lin, X. Sheldon, 2019. "A class of mixture of experts models for general insurance: Theoretical developments," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 111-127.
    31. Chai Fung, Tsz & Badescu, Andrei L. & Sheldon Lin, X., 2019. "A Class Of Mixture Of Experts Models For General Insurance: Application To Correlated Claim Frequencies," ASTIN Bulletin, Cambridge University Press, vol. 49(3), pages 647-688, September.
    32. Lluís Bermúdez & Dimitris Karlis & Isabel Morillo, 2020. "Modelling Unobserved Heterogeneity in Claim Counts Using Finite Mixture Models," Risks, MDPI, vol. 8(1), pages 1-13, January.
    33. Robert L. Winkler, 1968. "The Consensus of Subjective Probability Distributions," Management Science, INFORMS, vol. 15(2), pages 61-75, October.
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