메뉴 건너뛰기




Volumn 8, Issue 4, 1999, Pages 824-838

Calculation of Posterior Bounds Given Convex Sets of Prior Probability Measures and Likelihood Functions

Author keywords

Bayesian robustness analysis; Fractional programming; Lavine s algorithm; Lower and upper envelopes; White Snow algorithm

Indexed keywords


EID: 0033273449     PISSN: 10618600     EISSN: 15372715     Source Type: Journal    
DOI: 10.1080/10618600.1999.10474851     Document Type: Article
Times cited : (20)

References (46)
  • 3
  • 4
    • 0040616116 scopus 로고    scopus 로고
    • Numerical Robust Bayesian Analysis Under Generalized Moment Conditions
    • J. O. Berger, B. Betro, E. Moreno, L. R. Pericchi, F. Ruggeri, G. Salinetti, and L. Wasserman, Hayward, CA: Institute of Mathematical Statistics
    • Betrft, B., and Guglielmi, A. (1996), “Numerical Robust Bayesian Analysis Under Generalized Moment Conditions,” in Bayesian Robustness: Proceedings of the Workshop on Bayesian Robustness, Lecture Notes-Monograph Series (vol. 29), eds. J. O. Berger, B. Betro, E. Moreno, L. R. Pericchi, F. Ruggeri, G. Salinetti, and L. Wasserman, Hayward, CA: Institute of Mathematical Statistics, pp. 3-16.
    • (1996) Bayesian Robustness: Proceedings of the Workshop on Bayesian Robustness, Lecture Notes-Monograph Series , vol.29 , pp. 3-16
    • Betrft, B.1    Guglielmi, A.2
  • 5
    • 0008621136 scopus 로고
    • Decision Making With Interval Influence Diagrams
    • P. P. Bonissone, M. Henrion, L. N. Kanal, and J. F. Lemmer, North-Holland: Elsevier Science
    • Breese, J. S., and Fertig, K. W. (1991), “Decision Making With Interval Influence Diagrams,” in Uncertainty in Artificial Intelligence 6, eds. P. P. Bonissone, M. Henrion, L. N. Kanal, and J. F. Lemmer, North-Holland: Elsevier Science, pp. 467-478.
    • (1991) Uncertainty in Artificial Intelligence 6 , pp. 467-478
    • Breese, J.S.1    Fertig, K.W.2
  • 6
    • 0002061428 scopus 로고
    • Incremental Conditioning of Lower and Upper Probabilities
    • Chrisman, L. (1995), “Incremental Conditioning of Lower and Upper Probabilities,” International Journal of Approximate Reasoning, 13, 1-25.
    • (1995) International Journal of Approximate Reasoning , vol.13 , pp. 1-25
    • Chrisman, L.1
  • 7
    • 0008637688 scopus 로고    scopus 로고
    • Independence With Lower and Upper Probabilities
    • E. Horvitz and F. Jensen, San Francisco: Morgan Kaufmann
    • Chrisman, L. (1996a), “Independence With Lower and Upper Probabilities,” in XII Conference on Uncertainty in Artificial Intelligence, eds. E. Horvitz and F. Jensen, San Francisco: Morgan Kaufmann, pp. 169-177.
    • (1996) XII Conference on Uncertainty in Artificial Intelligence , pp. 169-177
    • Chrisman, L.1
  • 8
    • 0042126914 scopus 로고    scopus 로고
    • Propagation of 2-Monotone Lower Probabilities on an Undirected Graph
    • E. Horvitz and F. Jensen, San Francisco: Morgan Kaufmann
    • Chrisman, L. (1996b), “Propagation of 2-Monotone Lower Probabilities on an Undirected Graph,” in XII Conference on Uncertainty in Artificial Intelligence, eds. E. Horvitz and F. Jensen, San Francisco: Morgan Kaufmann, pp. 178-186.
    • (1996) XII Conference on Uncertainty in Artificial Intelligence , pp. 178-186
    • Chrisman, L.1
  • 9
    • 0002532555 scopus 로고
    • Independence Concepts for Convex Sets of Probabilities
    • P. Besnards and S. Hanks, San Francisco: Morgan Kaufmann
    • de Campos, L., and Moral, S. (1995), “Independence Concepts for Convex Sets of Probabilities,” in XI Conference on Uncertainty in Artificial Intelligence, eds. P. Besnards and S. Hanks, San Francisco: Morgan Kaufmann, pp. 108-115.
    • (1995) XI Conference on Uncertainty in Artificial Intelligence , pp. 108-115
    • De Campos, L.1    Moral, S.2
  • 10
    • 0000516376 scopus 로고
    • Upper and Lower Probabilities Induced by a Multivalued Mapping
    • Dempster, A. P. (1967), “Upper and Lower Probabilities Induced by a Multivalued Mapping," Annals of Mathematical Statistics 38, 325-339.
    • (1967) Annals of Mathematical Statistics , vol.38 , pp. 325-339
    • Dempster, A.P.1
  • 13
    • 38249032695 scopus 로고
    • Lower Probability Models for Uncertainty and Nondeterministic Processes
    • Fine, T. L. (1988), “Lower Probability Models for Uncertainty and Nondeterministic Processes,” Journal of Statistical Planning and Inference, 20, 389-411.
    • (1988) Journal of Statistical Planning and Inference , vol.20 , pp. 389-411
    • Fine, T.L.1
  • 14
    • 0028499410 scopus 로고
    • Anytime Deduction for Probabilistic Logic
    • Frisch, A. M., and Haddawy, P. (1994), “Anytime Deduction for Probabilistic Logic," Artificial Intelligence, 69, 93-122.
    • (1994) Artificial Intelligence , vol.69 , pp. 93-122
    • Frisch, A.M.1    Haddawy, P.2
  • 15
    • 51849177679 scopus 로고
    • Quasi-Bayesian Behaviour: A More Realistic Approach to Decision Making?
    • J. M. Bernardo, J. H. DeGroot, D. V. Lindley, and A. F. M. Smith, Valencia, Spain: University Press
    • Giron, F. J., and Rios, S. (1980), “Quasi-Bayesian Behaviour: A More Realistic Approach to Decision Making?" in Bayesian Statistics, eds. J. M. Bernardo, J. H. DeGroot, D. V. Lindley, and A. F. M. Smith, Valencia, Spain: University Press, pp. 17-38.
    • (1980) Bayesian Statistics , pp. 17-38
    • Giron, F.J.1    Rios, S.2
  • 17
    • 0023314059 scopus 로고
    • Bayesian and Non-Bayesian Evidential Updating
    • Kyburg Jr., H. E. (1987), “Bayesian and Non-Bayesian Evidential Updating," Artificial Intelligence, 31, 271-293.
    • (1987) Artificial Intelligence , vol.31 , pp. 271-293
    • Kyburg, H.E.1
  • 18
    • 0026852552 scopus 로고
    • Two Views of Belief: Belief as Generalized Probability and Belief as Evidence
    • Halpera, J. Y., and Fagin, R. (1992), “Two Views of Belief: Belief as Generalized Probability and Belief as Evidence,” Artificial Intelligence, 54, 275-317.
    • (1992) Artificial Intelligence , vol.54 , pp. 275-317
    • Halpera, J.Y.1    Fagin, R.2
  • 19
    • 0010072372 scopus 로고
    • Solving Mathematical Programming Problems With Fractional Objective Functions
    • S. Schaible and W. T. Ziemba, New York: Academic Press
    • Ibaraki, T. (1981), “Solving Mathematical Programming Problems With Fractional Objective Functions,” in Generalized Concavity in Optimization and Economics, eds. S. Schaible and W. T. Ziemba, New York: Academic Press, pp. 440-472.
    • (1981) Generalized Concavity in Optimization and Economics , pp. 440-472
    • Ibaraki, T.1
  • 22
    • 0000181744 scopus 로고
    • Sensitivity in Bayesian Statistics, the Prior and the Likelihood
    • Lavine, M. (1991), “Sensitivity in Bayesian Statistics, the Prior and the Likelihood,” Journal of the American Statistical Association, 86, 396-399.
    • (1991) Journal of the American Statistical Association , vol.86 , pp. 396-399
    • Lavine, M.1
  • 26
    • 0030284785 scopus 로고    scopus 로고
    • Computation of Best Bounds of Probabilities from Uncertain Data
    • Luo, C., Yu, C., Lobo, J., Wang, G., and Pham, T. (1996), “Computation of Best Bounds of Probabilities from Uncertain Data," Computational Intelligence, 12, 541-566.
    • (1996) Computational Intelligence , vol.12 , pp. 541-566
    • Luo, C.1    Yu, C.2    Lobo, J.3    Wang, G.4    Pham, T.5
  • 28
    • 0008643551 scopus 로고
    • Technical Report Serie A n. 23, Dipartamento di Statistica, Probabilita e Statistiche Applicate, Universita di Roma La Sapienza, Italy
    • Pacifico, M. P., Salinetti, G., and Tardella, L. (1994), "Fractional Optimization in Bayesian Robustness," Technical Report Serie A n. 23, Dipartamento di Statistica, Probabilita e Statistiche Applicate, Universita di Roma La Sapienza, Italy.
    • (1994) Fractional Optimization in Bayesian Robustness
    • Pacifico, M.P.1    Salinetti, G.2    Tardella, L.3
  • 31
    • 0030289946 scopus 로고    scopus 로고
    • Tighter Estimates for the Posteriors of Imprecise Prior and Conditional Probabilities
    • Salo, A. A. (1996), “Tighter Estimates for the Posteriors of Imprecise Prior and Conditional Probabilities,” Transactions on Systems, Man, and Cybernetics A 26, 820-825.
    • (1996) Transactions on Systems, Man, and Cybernetics A , vol.26 , pp. 820-825
    • Salo, A.A.1
  • 33
    • 21344454414 scopus 로고
    • A Representation of Partially Ordered Preferences
    • Seidenfeld, T., Schervish, M. J., and Kadane, J. B. (1995), “A Representation of Partially Ordered Preferences,” Annals of Statistics, 23, 2168-2217.
    • (1995) Annals of Statistics , vol.23 , pp. 2168-2217
    • Seidenfeld, T.1    Schervish, M.J.2    Kadane, J.B.3
  • 34
    • 0003095061 scopus 로고
    • Consistency in Statistical Inference and Decision
    • Ser. B
    • Smith, C. A. B. (1961), “Consistency in Statistical Inference and Decision," Journal of the Royal Statistical Society Ser. B, 23. 1-25.
    • (1961) Journal of the Royal Statistical Society , vol.23 , pp. 1-25
    • Smith, C.A.B.1
  • 35
    • 0026121940 scopus 로고
    • Improved Posterior Probability Estimates From Prior and Conditional Linear Constraint Systems
    • Snow, P. (1991), “Improved Posterior Probability Estimates From Prior and Conditional Linear Constraint Systems,” Transactions on Systems, Man, and Cybernetics A, 21, 464-469.
    • (1991) Transactions on Systems, Man, and Cybernetics A , vol.21 , pp. 464-469
    • Snow, P.1
  • 36
    • 0030241616 scopus 로고    scopus 로고
    • The Posterior Probabilities of Linearly Constrained Priors and Interval-Bounded Conditionals
    • Snow, P. (1996), “The Posterior Probabilities of Linearly Constrained Priors and Interval-Bounded Conditionals,” IEEE Transactions on Systems, Man and Cybernetics 26A, 655-659.
    • (1996) IEEE Transactions on Systems, Man and Cybernetics , vol.26A , pp. 655-659
    • Snow, P.1
  • 38
    • 0006420211 scopus 로고
    • Towards Precision of Probabilistic Bounds Propagation
    • D. Dubois, M. P. Wellman, B. D'Ambrosio, and P. Smets, San Francisco: Morgan Kaufmann
    • Thone, H., Guntzer, U., and KieBling, W. (1992), “Towards Precision of Probabilistic Bounds Propagation," in VIII Conference on Uncertainty in Artificial Intelligence, eds. D. Dubois, M. P. Wellman, B. D'Ambrosio, and P. Smets, San Francisco: Morgan Kaufmann, pp. 315-322.
    • (1992) VIII Conference on Uncertainty in Artificial Intelligence , pp. 315-322
    • Thone, H.1    Guntzer, U.2    Kiebling, W.3
  • 39
    • 0004202202 scopus 로고
    • Technical Report, Statistics Report 23, University of Warwick, Coventry
    • Walley, P. (1981), "Coherent Lower (and Upper) Probabilities," Technical Report, Statistics Report 23, University of Warwick, Coventry.
    • (1981) Coherent Lower (And Upper) Probabilities
    • Walley, P.1
  • 41
    • 0030146168 scopus 로고    scopus 로고
    • Measures of Uncertainty in Expert Systems
    • Walley, P. (1996), "Measures of Uncertainty in Expert Systems,” Artificial Intelligence 83, 1-58.
    • (1996) Artificial Intelligence , vol.83 , pp. 1-58
    • Walley, P.1
  • 42
    • 0000012623 scopus 로고
    • Prior Envelopes Based on Belief Functions
    • Wasserman, L. A. (1990), “Prior Envelopes Based on Belief Functions," Annals of Statistics, 18, 454-464.
    • (1990) Annals of Statistics , vol.18 , pp. 454-464
    • Wasserman, L.A.1
  • 43
    • 0000083758 scopus 로고
    • Recent Methodological Advances in Robust Bayesian Inference
    • J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, Cambridge, MA: Oxford University Press
    • Wasserman, L. A. (1992), “Recent Methodological Advances in Robust Bayesian Inference," in Bayesian Statistics 4, eds. J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, Cambridge, MA: Oxford University Press.
    • (1992) Bayesian Statistics , vol.4
    • Wasserman, L.A.1
  • 44
    • 0001225772 scopus 로고
    • Bayes' Theorem for Choquet Capacities
    • Wasserman, L. A., and Kadane, J. B. (1990), “Bayes' Theorem for Choquet Capacities,” Annals of Statistics 18, 1328-1339.
    • (1990) Annals of Statistics , vol.18 , pp. 1328-1339
    • Wasserman, L.A.1    Kadane, J.B.2
  • 45
    • 0022754616 scopus 로고
    • A Posteriori Representations Based on Linear Inequality Descriptions of A Priori and Conditional Probabilities
    • White, C. C. (1986), “A Posteriori Representations Based on Linear Inequality Descriptions of A Priori and Conditional Probabilities,” IEEE Transactions on Systems, Man and Cybernetics SMC-16, 570-573.
    • (1986) IEEE Transactions on Systems, Man and Cybernetics , vol.SMC-16 , pp. 570-573
    • White, C.C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.