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Shrinking the Variance in Experts’ “Classical” Weights Used in Expert Judgment Aggregation

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  • Gayan Dharmarathne

    (Department of Statistics, University of Colombo, Colombo 00300, Sri Lanka)

  • Gabriela F. Nane

    (Delft Institute of Applied Mathematics, Delft University of Technology, 2628 CD Delft, The Netherlands)

  • Andrew Robinson

    (Centre of Excellence for Biosecurity Risk Analysis, School of BioSciences, The University of Melbourne, Melbourne, VIC 3010, Australia)

  • Anca M. Hanea

    (Centre of Excellence for Biosecurity Risk Analysis, School of BioSciences, The University of Melbourne, Melbourne, VIC 3010, Australia)

Abstract

Mathematical aggregation of probabilistic expert judgments often involves weighted linear combinations of experts’ elicited probability distributions of uncertain quantities. Experts’ weights are commonly derived from calibration experiments based on the experts’ performance scores, where performance is evaluated in terms of the calibration and the informativeness of the elicited distributions. This is referred to as Cooke’s method, or the classical model (CM), for aggregating probabilistic expert judgments. The performance scores are derived from experiments, so they are uncertain and, therefore, can be represented by random variables. As a consequence, the experts’ weights are also random variables. We focus on addressing the underlying uncertainty when calculating experts’ weights to be used in a mathematical aggregation of expert elicited distributions. This paper investigates the potential of applying an empirical Bayes development of the James–Stein shrinkage estimation technique on the CM’s weights to derive shrinkage weights with reduced mean squared errors. We analyze 51 professional CM expert elicitation studies. We investigate the differences between the classical and the (new) shrinkage CM weights and the benefits of using the new weights. In theory, the outcome of a probabilistic model using the shrinkage weights should be better than that obtained when using the classical weights because shrinkage estimation techniques reduce the mean squared errors of estimators in general. In particular, the empirical Bayes shrinkage method used here reduces the assigned weights for those experts with larger variances in the corresponding sampling distributions of weights in the experiment. We measure improvement of the aggregated judgments in a cross-validation setting using two studies that can afford such an approach. Contrary to expectations, the results are inconclusive. However, in practice, we can use the proposed shrinkage weights to increase the reliability of derived weights when only small-sized experiments are available. We demonstrate the latter on 49 post-2006 professional CM expert elicitation studies.

Suggested Citation

  • Gayan Dharmarathne & Gabriela F. Nane & Andrew Robinson & Anca M. Hanea, 2023. "Shrinking the Variance in Experts’ “Classical” Weights Used in Expert Judgment Aggregation," Forecasting, MDPI, vol. 5(3), pages 1-14, August.
  • Handle: RePEc:gam:jforec:v:5:y:2023:i:3:p:29-535:d:1223595
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    References listed on IDEAS

    as
    1. John Quigley & Abigail Colson & Willy Aspinall & Roger M. Cooke, 2018. "Elicitation in the Classical Model," International Series in Operations Research & Management Science, in: Luis C. Dias & Alec Morton & John Quigley (ed.), Elicitation, chapter 0, pages 15-36, Springer.
    2. Cooke, Roger M. & Marti, Deniz & Mazzuchi, Thomas, 2021. "Expert forecasting with and without uncertainty quantification and weighting: What do the data say?," International Journal of Forecasting, Elsevier, vol. 37(1), pages 378-387.
    3. 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.
    4. Bing-Yi Jing & Zhouping Li & Guangming Pan & Wang Zhou, 2016. "On SURE-Type Double Shrinkage Estimation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1696-1704, October.
    5. Deniz Marti & Thomas A. Mazzuchi & Roger M. Cooke, 2021. "Are Performance Weights Beneficial? Investigating the Random Expert Hypothesis," International Series in Operations Research & Management Science, in: Anca M. Hanea & Gabriela F. Nane & Tim Bedford & Simon French (ed.), Expert Judgement in Risk and Decision Analysis, chapter 0, pages 53-82, Springer.
    6. Anca M. Hanea & Gabriela F. Nane, 2021. "An In-Depth Perspective on the Classical Model," International Series in Operations Research & Management Science, in: Anca M. Hanea & Gabriela F. Nane & Tim Bedford & Simon French (ed.), Expert Judgement in Risk and Decision Analysis, chapter 0, pages 225-256, Springer.
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