On coherent immediate prediction: Connecting two theories of imprecise probability

ISIPTA 2007 - Proceedings of the 5th International Symposium on Imprecise Probability: Theories and Applications

Volumn , Issue , 2007, Pages 97-106

  De Cooman, Gert ^a   Hermans, Filip ^a  

^a GHENT UNIVERSITY   (Belgium)

Author keywords

Coherence; Conglomerability; Event tree; Game theoretic probability; Hoeffding's inequality; Immediate prediction; Imprecise probabilities; Law of large numbers; Lower prevision; Prequential principle

Indexed keywords

CONGLOMERABILITY; EVENT TREES; GAME-THEORETIC; HOEFFDING'S INEQUALITY; IMMEDIATE PREDICTION; IMPRECISE PROBABILITIES; LAW OF LARGE NUMBERS; LOWER PREVISION; PREQUENTIAL PRINCIPLE;

COHERENT LIGHT; FORECASTING; GAME THEORY;

PROBABILISTIC LOGICS;

EID: 62749166496     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (24)

1. A. Ph. Dawid. Statistical theory: The prequential approach. Journal of the Royal Statistical Society, Series A, 147:278-292, 1984.
2. A. Ph. Dawid and V. G. Vovk. Prequential probability: principles and properties. Bernoulli, 5:125-162, 1999.
3. B. de Finetti. Teoria delle Probabilità. Einaudi, Turin, 1970.
4. B. de Finetti. Theory of Probability. John Wiley & Sons, Chichester, 1974-1975. English translation of, two volumes.
5. P. Gärdenfors and N.-E. Sahlin. Decision, Probability, and Utility. Cambridge University Press, Cambridge, 1988.
6. M. Goldstein. The prevision of a prevision. Journal of the American Statistical Society, 87:817-819, 1983.
7. W. Hoeffding. Probability inequalities for sums of bounded random variables. Journal of the Americal Statistical Association, 58:13-30, 1963.
8. H. E. Kyburg Jr. and H. E. Smokler, editors. Studies in Subjective Probability. Wiley, New York, 1964. Second edition (with new material) 1980.
9. E. Miranda and G. de Cooman. Marginal extension in the theory of coherent lower previsions. International Journal of Approximate Reasoning, 2006. In press.
10. F. P. Ramsey. Truth and probability (1926). In R. B. Braithwaite, editor, The Foundations of Mathematics and other Logical Essays, chapter VII, pages 156- 198. Kegan, Paul, Trench, Trubner & Co., London, 1931. Reprinted in [8] and [5].
11. G. Shafer. Bayes's two arguments for the Rule of Conditioning. The Annals of Statistics, 10:1075-1089, 1982.
12. G. Shafer. A subjective interpretation of conditional probability. Journal of Philosophical Logic, 12:453- 466, 1983.
13. G. Shafer. Conditional probability. International Statistical Review, 53:261-277, 1985.
14. G. Shafer. The Art of Causal Conjecture. The MIT Press, Cambridge, MA, 1996.
15. G. Shafer. The significance of Jacob Bernoulli's Ars Conjectandi for the philosophy of probability today. Journal of Econometrics, 75:15-32, 1996.
16. G. Shafer, P. R. Gillett, and R. Scherl. The logic of events. Annals of Mathematics and Artificial Intelligence, 28:315-389, 2000.
17. G. Shafer, P. R. Gillett, and R. B. Scherl. A new understanding of subjective probability and its generalization to lower and upper prevision. International Journal of Approximate Reasoning, 33:1-49, 2003.
18. G. Shafer and V. Vovk. Probability and Finance: It's Only a Game! Wiley, New York, 2001.
19. V. Vovk, A. Gammerman, and G. Shafer. Algorithmic learning in a Random World. Springer, New York, 2005.
20. P. Walley. Statistical Reasoning with Imprecise Probabilities. Chapman and Hall, London, 1991.
21. P. Walley. Towards a unified theory of imprecise probability. International Journal of Approximate Reasoning, 24:125-148, 2000.
22. L. Wasserman. All of Statistics. Springer, New York, 2004.
23. P.M.Williams. Notes on conditional previsions. Technical report, School of Mathematical and Physical Science, University of Sussex, UK, 1975.
24. P. M.Williams. Notes on conditional previsions. International Journal of Approximate Reasoning, 44:366- 383, 2007. Revised journal version of [23].