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On coherent immediate prediction: connecting two theories of imprecise probability

Gert De Cooman (UGent) and Filip Hermans (UGent)
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Abstract
We give an overview of two approaches to probabiliity theory where lower and upper probabilities, rather than probabilities, are used: Walley's behavioural theory of imprecise probabilities, and Shafer and Vovk's game-theoretic account of probability. We show that the two theories are more closely related than would be suspected at first sight, and we establish a correspondence between them that (i) has an interesting interpretation, and (ii) allows us to freely import results from one theory into the other. Our approach leads to an account of immediate prediction in the framework of Walley's theory, and we prove an interesting and quite general version of the weak law of large numbers.
Keywords
imprecise probabilities, Game-theoretic probability, coherence, conglomerability, event tree, lower prevision, immediate prediction, Prequential Principle, law of large numbers, Hoeffding's inequality, CONDITIONAL-PROBABILITY

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MLA
De Cooman, Gert, and Filip Hermans. “On Coherent Immediate Prediction: Connecting Two Theories of Imprecise Probability.” ISIPTA 07-PROCEEDINGS OF THE FIFTH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITY:THEORIES AND APPLICATIONS. Ed. G De Cooman, J Vejnarová, & M Zaffalon. SIPTA - International Society for Imprecise Probability: Theories and Applications, 2007. 97–106. Print.
APA
De Cooman, G., & Hermans, F. (2007). On coherent immediate prediction: connecting two theories of imprecise probability. In G De Cooman, J. Vejnarová, & M. Zaffalon (Eds.), ISIPTA 07-PROCEEDINGS OF THE FIFTH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITY:THEORIES AND APPLICATIONS (pp. 97–106). Presented at the 5th International Symposium on Imprecise Probability, SIPTA - International Society for Imprecise Probability: Theories and Applications.
Chicago author-date
De Cooman, Gert, and Filip Hermans. 2007. “On Coherent Immediate Prediction: Connecting Two Theories of Imprecise Probability.” In ISIPTA 07-PROCEEDINGS OF THE FIFTH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITY:THEORIES AND APPLICATIONS, ed. G De Cooman, J Vejnarová, and M Zaffalon, 97–106. SIPTA - International Society for Imprecise Probability: Theories and Applications.
Chicago author-date (all authors)
De Cooman, Gert, and Filip Hermans. 2007. “On Coherent Immediate Prediction: Connecting Two Theories of Imprecise Probability.” In ISIPTA 07-PROCEEDINGS OF THE FIFTH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITY:THEORIES AND APPLICATIONS, ed. G De Cooman, J Vejnarová, and M Zaffalon, 97–106. SIPTA - International Society for Imprecise Probability: Theories and Applications.
Vancouver
1.
De Cooman G, Hermans F. On coherent immediate prediction: connecting two theories of imprecise probability. In: De Cooman G, Vejnarová J, Zaffalon M, editors. ISIPTA 07-PROCEEDINGS OF THE FIFTH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITY:THEORIES AND APPLICATIONS. SIPTA - International Society for Imprecise Probability: Theories and Applications; 2007. p. 97–106.
IEEE
[1]
G. De Cooman and F. Hermans, “On coherent immediate prediction: connecting two theories of imprecise probability,” in ISIPTA 07-PROCEEDINGS OF THE FIFTH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITY:THEORIES AND APPLICATIONS, Prague, Czech Republic, 2007, pp. 97–106.
@inproceedings{371960,
  abstract     = {We give an overview of two approaches to probabiliity theory where lower and upper probabilities, rather than probabilities, are used: Walley's behavioural theory of imprecise probabilities, and Shafer and Vovk's game-theoretic account of probability. We show that the two theories are more closely related than would be suspected at first sight, and we establish a correspondence between them that (i) has an interesting interpretation, and (ii) allows us to freely import results from one theory into the other. Our approach leads to an account of immediate prediction in the framework of Walley's theory, and we prove an interesting and quite general version of the weak law of large numbers.},
  author       = {De Cooman, Gert and Hermans, Filip},
  booktitle    = {ISIPTA 07-PROCEEDINGS OF THE FIFTH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITY:THEORIES AND APPLICATIONS},
  editor       = {De Cooman, G and Vejnarová, J and Zaffalon, M},
  isbn         = {978-80-86742-20-5},
  keywords     = {imprecise probabilities,Game-theoretic probability,coherence,conglomerability,event tree,lower prevision,immediate prediction,Prequential Principle,law of large numbers,Hoeffding's inequality,CONDITIONAL-PROBABILITY},
  language     = {eng},
  location     = {Prague, Czech Republic},
  pages        = {97--106},
  publisher    = {SIPTA - International Society for Imprecise Probability: Theories and Applications},
  title        = {On coherent immediate prediction: connecting two theories of imprecise probability},
  year         = {2007},
}

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