Coherent conditional probabilities and proper scoring rules

ISIPTA 2011 - Proceedings of the 7th International Symposium on Imprecise Probability: Theories and Applications

Volumn , Issue , 2011, Pages 189-198

  Gilio, Angelo ^a   Sanfilippo, Giuseppe ^b  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b UNIVERSITY OF PALERMO   (Italy)

Author keywords

Admissibility; Bregman divergence; Coherence; Conditional probability assessments; Conditional scoring rules; Gcoherence; Imprecise probability assessments; Penalty criterion; Proper scoring rules; Strong dominance; Total coherence; Weak dominance

Indexed keywords

ADMISSIBILITY; BREGMAN DIVERGENCES; CONDITIONAL PROBABILITIES; CONDITIONAL SCORING RULES; GCOHERENCE; IMPRECISE PROBABILITIES; PENALTY CRITERION; PROPER SCORING RULES; STRONG DOMINANCES; WEAK DOMINANCES;

COHERENT LIGHT;

PROBABILITY;

EID: 84866033395     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (37)

1. G. Agro, F. Lad, G. Sanfilippo. Sequentially forecasting economic indices using mixture linear combinations of EP distributions. Journal of Data Science, 8(1):101-126, 2010.
2. V. Biazzo, A. Gilio. A generalization of the fundamental theorem of de Finetti for imprecise conditional probability assessments, International Journal of Approximate Reasoning 24, 251-272, 2000.
3. V. Biazzo, A. Gilio, G. Sanfilippo. Coherence Checking and Propagation of Lower Probability Bounds, Soft Computing 7, 310-320, 2003.
4. V. Biazzo, A. Gilio, G. Sanfilippo. Generalized coherence and connection property of imprecise conditional previsions. In: Proceedings of 12th Information Processing and Management of Uncertainty in Knowledge-Based Systems Conference, IPMU 2008, Malaga, Spain, June 22 - 27, 907-914, 2008.
5. G. W. Brier. Verification of forecasts expressed in terms of probability, Monthly Weather Review, 78:1-3, 1950.
6. Y. Censor, S.A. Zenios. Parallel Optimization: Theory, Algorithms, and Applications. Oxford Univ. Press, Oxford, 1997.
7. A. Capotorti, G. Regoli, F. Vattari. Correction of incoherent conditional probability assessments. International Journal of Approximate Reasoning, 51:718-727, 2010.
8. G. Coletti, R. Scozzafava. Probabilistic logic in a coherent setting. Kluwer, Dordrecht, 2002.
9. B. de Finetti. Does it make sense to speak of 'good probability appraisers'? In: The scientist speculates: an anthology of of partly-baked ideas, I. J. Good (ed.), Heinemann, London, 357-364, 1962.
10. B. de Finetti. Probabilita composte e teoria delle decisioni. Rendiconti di Matematica, 23:128-134, 1964.
11. B. de Finetti. Teoria delle probabilita, voll. 1, 2. Einaudi, Torino, 1970, (Engl. transl.: Theory of Probability, voll. 1-2, Wiley, Chichester, 1974, 1975).
12. B. de Finetti. The Role of 'Dutch Books' and of 'Proper Scoring Rules'. The British Journal for the Philosophy of Science, 32(1):55-56, 1981.
13. D. Gale. The theory of linear economic models. McGraw-Hill, New York, 1960.
14. A. Gilio. Probabilita condizionate C0-coerenti. Rendiconti di Matematica, Serie VII, 9:277-295, 1989.
15. A. Gilio. Criterio di penalizzazione e condizioni di coerenza nella valutazione soggettiva della probabilita. Boll. Un. Mat. Ital., [7a] 4-B(3): 645-660, 1990.
16. A. Gilio. C0-Coherence and Extension of Conditional Probabilities. In: Bayesian Statistics 4, J. M. Bernardo, J. O. Berger, A. P. Dawid, A. F. M. Smith (eds.), Oxford University Press, 633- 640, 1992.
17. A. Gilio. Algorithms for precise and imprecise conditional probability assessments. In: Mathematical Models for Handling Partial Knowledge in Artificial Intelligence, G. Coletti, D. Dubois, R. Scozzafava (eds.), Plenum Press, New York, 231-254, 1995.
18. A. Gilio. Algorithms for conditional probability assessments. In: Bayesian Analysis in Statistics and Econometrics: Essays in Honor of Arnold Zellner, D. A. Berry, K. M. Chaloner, J. K. Geweke (eds.), John Wiley, 29-39, 1996.
19. A. Gilio, S. Ingrassia. Totally coherent setvalued probability assessments. Kybernetika 34(1): 3-15, 1998.
20. T. Gneiting, A. Raftery. Strictly proper scoring rules, prediction and estimation. Journal of the American Statistical Association, 102(477):359- 378, 2007.
21. I. J. Good. Rational decisions. J. Roy. Statist. Soc., 14:107-114, 1952.
22. S. Holzer. On coherence and conditional prevision. Boll. Un. Mat. Ital., 4(6):441-460, 1985.
23. A. D. Hendrickson, R. J. Buehler. Proper scores for probability forecasters. Ann. Math. Statist. 42:1916-1921, 1971.
24. V. R. R. Jose, R. F. Nau, R. L. Winkler. Scoring Rules, Generalized Entropy, and Utility Maximization, Operations Research, 56(5):1146-1157, 2008.
25. F. Lad. Operational Subjective Statistical Methods: A mathematical, philosophical, and historical introduction. John Wiley, New York, 1996.
26. D. V. Lindley. Scoring rules and the inevitability of probability. Int. Statist. Rev., 50:1-11, 1982.
27. J. B. Predd, R. Seiringer, E. H. Lieb, D. N. Osherson, H. V. Poor, S. R. Kulkarni. Probabilistic Coherence and Proper Scoring Rules. IEEE T. Inform. Theory, 55:4786-4792, 2009.
28. J. McCarthy. Measures of the value of information. Proceedings of the National Academy of Sciences, 42:654-655, 1956.
29. R. F. Nau, V. R. R. Jose, R. L. Winkler. Scoring Rules, Entropy, and Imprecise Probabilities. In: Proceedings of the 5th International Symposium on Imprecise Probabilities and their Applications, ISIPTA07, Prague, Czech Republic, 307-316, 2007.
30. E. Regazzini. Finitely additive conditional probabilities. Rend. Sem. Mat. Fis. Milano, 55:69- 89, 1985.
31. G. Sanfilippo, G. Agro, F. Lad. Assessing fat-tailed sequential forecast distributions for the Dow-Jones index with logarithmic scoring rules. In: Proc. of 56th Session of the International Statistical Institute, Lisbon, 22-29, August, 2007.
32. L. J. Savage. Elicitation of personal probabilities and expectations. J. Amer. Statist. Assoc., 66:783-801, 1971.
33. M. J. Schervish, T. Seidenfeld, J. B. Kadane. Proper Scoring Rules, Dominated Forecasts, and Coherence. Decision Analysis, 6(4):202- 221, 2009.
34. P. Walley, R. Pelessoni, P. Vicig. Direct Algorithms for Checking Coherence and Making Inferences from Conditional Probability Assessments, Journal of Statistical Planning and Inference, 126(1), 119-151, 2004.
35. P. M. Williams. Notes on conditional previsions, Technical report, University of Sussex 1975 Reprinted in a revised form in: International Journal of Approximate Reasoning, 44(3):366- 383, 2007.
36. R. L. Winkler. Scoring rules and the evaluation of probability assessors. J. Amer. Statist. Assoc., 64:1073-1078, 1969.
37. R. L. Winkler. Scoring rules and the evaluation of probabilities. Test 5(1):1-60, 1996.