Journal of the Italian Statistical Society

, Volume 1, Issue 1, pp 67–76 | Cite as

Incomplete probability assessments in decision analysis

  • Angelo Gilio
Article
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Summary

In analysing a decision problem, in a situation ofpartial knowledge, a decision maker may be reluctant to assign acomplete probability distribution on the relevant states of nature. In order to face this difficulty, several methods, based onindeterminate probabilities or probabilityintervals, have been proposed in the literature. In this paper, arguing that it is meaningless to judge probabilistic assessments ascorrect orwrong, it is maintained that onlycoherence has anobjective andsignificant role. Then to overcome practical difficulties, an approach based on thesubjective methodology and on the use ofnumerical andqualitative probabilities, is outlined.

Keywords

partial knowledge incomplete assessments subjective probability coherent numerical and qualitative evaluations coherent extensions generalized atoms 
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References

  1. Bruno G. andGilio A., (1980), Applicazione del metodo del simplesso al teorema fondamentale per le probabilità nella concezione soggettiva,Statistica, 40, 337–344.MATHMathSciNetGoogle Scholar
  2. Coletti G., (1990), Coherent qualitative probability,J. of Math. Psychol., 34, 297–310.MATHCrossRefMathSciNetGoogle Scholar
  3. Coletti G., Gilio A. andScozzafava R., (1990), Coherent qualitative probability and uncertainty in Artificial Intelligence,Proc. of The 8th Int. Congr. of Cybernetics and Systems, vol. 1, ed. C. N. Manikopoulos, June 11–15, 1990, New York, 132–138.Google Scholar
  4. Coletti G., Gilio A. andScozzafava R., (1991), Conditional events with vague information in expert systems,Lectures Notes in Computer Science, Eds. B. Bouchon-Meunier, R. R. Yager, L. A. Zadeh), Springer, n. 521, 106–114.Google Scholar
  5. De Finetti, B., (1970),Teoria delle probabilità, Torino, Einaudi.Google Scholar
  6. Fishburn P. C., (1965), Analysis of decisions with incomplete knowledge of probabilities,Oper. Res. 13, 217–237.MATHMathSciNetGoogle Scholar
  7. Gilio A., (1990a), Criterio di penalizzazione e condizioni di coerenza nella valutazione soggettiva della probabilità,Boll. Un. Mat. Ital., vol. 4-B, Serie 7a, 645–660.MATHMathSciNetGoogle Scholar
  8. Gilio A., (1990b), Analisi delle decisioni e probabilità qualitativa,Atti del XIV Convegno A.M.A.S.E.S., Pescara, 13–15 Settembre 1990, 345–352.Google Scholar
  9. Gilio A., (1992), Co—Coherence and extensions of conditional probabilities, Bayesian Statistics 4, J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, (Eds.), Oxford University Press, 1–8.Google Scholar
  10. Gilio A. andScozzafava R., (1988), Le probabilità condizionate coerenti nei sistemi esperti,Atti delle giornate AIRO su Ricerca Operative e Intelligenza Artificiale, Pisa, Centro di Ricerca IBM, 317–330.Google Scholar
  11. Giron F. J. andRios F., (1980), Quasi-Bayesian behavior: A more realistic approach to decision making?,Bayesian Statistic II, eds. J. M. Bernardo, M. H. De Groot, D. V. Lindley, A. F. M. Smith (Univ. Press, Valencia), 17–38.Google Scholar
  12. Good I. J., (1980), Subjective probability as the measure of a non-measureable set,Studies in Subjective Probability (eds. H. E. Kyburg and H. E. Smokler), sec. ed., R. Krieger, New York.Google Scholar
  13. Holzer S., (1985), On coherence and conditional prevision,Boll. Un. Mat. Ital., Vol. IV, Serie VI, 441–460.MathSciNetGoogle Scholar
  14. Lad F. R., Dickey J. M. andRahman M. A., (1990), The Fundamental Theorem of Prevision,Statistica, anno L, 1, 19–38.MathSciNetGoogle Scholar
  15. Nau R. F., (1989), Decision Analysis with Indeterminate or Incoherent Probabilities,Annals of Operations Research 19, 375–403.MATHCrossRefMathSciNetGoogle Scholar
  16. Nilsson N. J., (1986), Probabilitistic Logic,Artificial Intelligence, 28, 71–87.MATHCrossRefMathSciNetGoogle Scholar
  17. Paass G., (1988), Probabilistic logic,Non-standard logics for automated reasoning, eds. P. Smets, E. H. Mamdani, D. Dubois, H. Prade, 213–51, New York, Academic Press.Google Scholar
  18. Regazzini E., (1985), Finitely additive conditional probabilities,Rend. Sem. Mat. Fis. Milano, 55, 69–89.MATHMathSciNetCrossRefGoogle Scholar
  19. Smith C. A. B., (1961), Consistency in statistical inference and decision,J. Roy. Stat. Soc. B23, 1, 1–37.Google Scholar
  20. Williams P. M., (1976), Indeterminate probabilities,Formal Methods in the Methodology of Empirical Sciences, ed. M. Przlecki, K. Szaniawki and R. Wojciki (Ossolineum and Reidel), Dordecht, Holland, 229–246.Google Scholar

Copyright information

© Societa Italiana di Statistica 1992

Authors and Affiliations

  • Angelo Gilio
    • 1
  1. 1.Dipartimento di Metodi e Modelli MatematiciUniversità «La Sapienza» di RomaRomaItaly

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