Skip to main content
SpringerLink
Log in

Fiducial inference in combining expert judgements

  • Statistical Methods
  • Published:
Statistical Methods and Applications Aims and scope Submit manuscript

Abstract

In the expert use problem, hierarchical models provide an ideal perspective for classifying understanding and generalising the aggregative algoithms suitable to compose experts' opinions in a single synthesis distribution. After suggesting to look at Peter A. Morris' (1971, 1974, 1977) Bayesian model in such a light, this paper addresses the problem of modelling the multidimensional ‘performance function’, which encodes aggregator's beliefs about each expert's assessment ability and the degree of dependence among the experts. Whenever the aggregator has not an empirically founded probability distribution for the experts' performances, the proposed fiducial procedure provides a rational and very flexible tool for enabling the performance function to be specified with a relatively small number of assessments: moreover, it warrants aggregator's beliefs about the experts in terms of personal long run frequencies.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Agti P (1997) Stime fiduciali di probabilìtà incognite. StatisticaLVII (3), 383–396

    Google Scholar 

  • Agati P (1998) Stime fiduciali di probabilità nell'aggregazione bayesiana di informazioni. StatisticaLVIII (4), 655–668

    Google Scholar 

  • Aitchison J, Brown JAC (1973) The lognormal distribution. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Buehler, RJ (1980) Fiducial inference. In Fienberg SE, Hinkley DV (eds.) R.A. Fisher: an appreciation. Springer, Berlin Heidelberg New York

    Google Scholar 

  • Clemen, RT (1986) Calibration and the aggregation of probabilities. Management Science32, 312–314

    Google Scholar 

  • Clemen, RT, Fisher GW, Winkler RL (2000) Assessing dependence: some experimental results. Management Science46, 1100–1115

    Article  Google Scholar 

  • Clemen, RT, Winkler RL (1985) Limits for the precision and value of information from dependent sources. Operation Research33, 427–442

    MATH  Google Scholar 

  • Clemen, RT, Winkler RL (1990) Unanimity and compromise among probability forecasters. Management Science36: 767–779

    MATH  Google Scholar 

  • Clemen, RT, Winkler RL (1993) Aggregating point estimates. A flexible modeling approach. Management Science39, 501–515

    MATH  Google Scholar 

  • Clemen, RT, Winkler RL (1999) Combining probability distributions from experts in risk analysis. Risk Analysis19, 187–203

    Google Scholar 

  • Cooke RM (1991) Experts in uncertainty. Opinion and subjective probability in science. Oxford University Press, Oxford

    Google Scholar 

  • Dawid AP (1982) The well-calibrated Bayesian. Journal of the American Statistical Association77, 605–613

    Article  MATH  MathSciNet  Google Scholar 

  • De Finetti B (1937) La prévision: ses lois logiques, ses sources subjectives. Annals de l'Institute Henry Poincaré7, 1–60 [Translated: (1963) Foresight: its logical laws, its subjective sources. In: Kyburg, Smokler (eds.) Studies in subjective probability, pp. 97–158, Wiley, New York]

    MATH  Google Scholar 

  • De Finetti B (1954) Media di decisioni e media di opinioni. Bulletin of the International Statistical InstituteXXXIV, 1–14

    Google Scholar 

  • Fisher RA (1930) Inverse probability. Proceedings of the Cambridge Philosophical Society26, 528–535

    Article  MATH  Google Scholar 

  • Fisher RA (1935) The fiducial argument in statistical inference. Annals of Eugenics6, 391–398

    Google Scholar 

  • Fisher RA (1956, second edition 1959) Statistical methods and scientific inference. Oliver & Boyd, Edinburgh

    MATH  Google Scholar 

  • Fisher RA (1957) The underworld of probability. Sankhya18, 201–210

    MATH  Google Scholar 

  • Freeling ANS (1981) Reconciliation of multiple probability assessments. Organizational behavior and human performance28, 395–414

    Article  Google Scholar 

  • French S (1980) Updating of belief in the light of someone else's opinion. Journal of the Royal Statistical Society A143, 43–48

    MATH  MathSciNet  Google Scholar 

  • French S (1985) Group consensus probability distributions: a critical survey. In: Bernardo JM et al., (eds.) Bayesian statistics 2, pp. 183–201., Elsevier Science Publishers B.V., North-Holland, Amsterdam

    Google Scholar 

  • French S (1986) Calibration and the expert problem. Management Science32, 315–321

    Google Scholar 

  • Gelfand AE, Mallick BK, Dey DK (1995) Modeling expert opinion rising as a partial probabilistic specification Journal of American Statistical Association90, 598–604

    Article  MATH  MathSciNet  Google Scholar 

  • Genest C, Schervish MJ (1985) Modeling expert judgments for Bayesian updating. Annals of Statistics13, 1198–1212

    MATH  MathSciNet  Google Scholar 

  • Genest, C., Zidek, JV (1986) Combining probability distributions: a critique and an annotated bibliography. Statistical Science,1, 114–148

    MATH  MathSciNet  Google Scholar 

  • Gokhale DV, Press SJ (1982) Assessment of a prior distribution for the correlation coefficient in a bivariate normal distribution. Journal of the Royal Statistical Society A145, 237–249

    MATH  Google Scholar 

  • Kalbfleisch JG (1979) Probability and statistical inference, vol.I. Springer, Berlin Heidelberg New York

    Google Scholar 

  • Lindley DV (1982) The improvement of probability judgements. Journal of the Royal Statistical Society A145, 117–126

    MATH  MathSciNet  Google Scholar 

  • Lindley DV (1983) Reconciliation of probability distributions. Operations Research,31, 866–880

    MATH  MathSciNet  Google Scholar 

  • Lindley DV (1985) Reconciliation of discrete probability distributions. In: Bernardo JM et al. (eds.) Bayesian statistics 2, pp. 375–390. Elsevier Science Publishers B. V., North-Holland, Amsterdam

    Google Scholar 

  • Lindley DV (1986) Another look at an axiomatic approach to expert resolution. Management Science32, 303–306

    Google Scholar 

  • Lindley DV (1990) The 1988 Wald Memorial Lectures: the present position in Bayesian statistics. Statistical Science5, 44–89

    MATH  MathSciNet  Google Scholar 

  • Lindley DV, Tversky A, Brown RV (1979) On the reconciliation of probability assessments. Journal of the Royal Statistical Society A142, 146–180

    MATH  MathSciNet  Google Scholar 

  • Morris CN, Normand SL (1992) Hierarchical models for combining information and for meta-analyses. In: Bernardo JM et al. (eds.) Bayesian statistics 4, pp. 321–344. Oxford University Press, Oxford

    Google Scholar 

  • Morris PA (1971) Bayesian expert resolution. Ph.D. Dissertation, Department of Engineering-Economic Systems, Stanford University

  • Morris PA (1974) Decision analysis expert use. Management Science20, 1233–1241

    MATH  Google Scholar 

  • Morris PA (1977) Combining expert judgements: a Bayesian approach. Management Science23, 679–693

    MATH  Google Scholar 

  • Morris PA (1983) An axiomatic approach to expert resolution. Management Science29, 24–32

    Google Scholar 

  • Morris PA (1986) Observations on expert resolution. Management Science32, 321–328

    Google Scholar 

  • Spiegelhalter DJ, Cowell RG (1992) Learning in probabilistic expert systems. In: Bernardo JM et al. (eds.) Bayesian statistics 4, pp. 447–465. Oxford University Press, Oxford

    Google Scholar 

  • Winkler RL, (1981) Combining probability distributions from dependent information sources. Management Science27, 479–488

    Article  MATH  MathSciNet  Google Scholar 

  • Winkler RL (1986) Expert resolution. Management Science32, 298–303

    Google Scholar 

  • Winkler RL, Clemen RT (1992) Sensitivity of weights in combining forecasts. Operations Research40, 609–614

    MATH  Google Scholar 

  • Wright G, Ayton P (1987) Judsemental forecasting. Wiley & Sons, New York

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Sciencze Statistiche, University of Bologna, Via delle Belle Arti 41, 40126, Bologna, Italy

    Paola Monari & Patrizia Agati

Authors
  1. Paola Monari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Patrizia Agati
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research supported by COFIN-99 grants.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Monari, P., Agati, P. Fiducial inference in combining expert judgements. Statistical Methods & Applications 10, 81–97 (2001). https://doi.org/10.1007/BF02511641

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02511641

Key words

Search

Navigation