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Foundations of neo-Bayesian statistics

  • Amarante, Massimiliano

We study an axiomatic model of preferences, which contains as special cases Subjective Expected Utility, Choquet Expected Utility, Maxmin and Maxmax Expected Utility and many other models. First, we give a complete characterization of the class of functionals representing these preferences. Then, we show that any such functional can be represented as a Choquet integral where is the canonical mapping from the space of bounded [Sigma]-measurable functions into the space of weak*-continuous affine functions on a weak*-compact, convex set of probability measures on [Sigma]. Conversely, any preference relation defined by means of such functionals satisfies the axioms of the model we study. Different properties of the capacity give rise to different models. Our result shows that the idea of Choquet integration is general enough to embrace all the models mentioned above. In doing so, it widens the range of applicability of well-known procedures in robust statistics theory such as the Neyman-Pearson lemma for capacities [P.J. Huber, V. Strassen, Minimax tests and the Neyman-Pearson lemma for capacities, Ann. Statist. 1 (1973) 251-263], Bayes' theorem for capacities [J.B. Kadane, L. Wasserman, Bayes' theorem for Choquet capacities, Ann. Statist. 18 (1990) 1328-1339] or of results like the Law of Large numbers for capacities [F. Maccheroni, M. Marinacci, A strong law of large numbers for capacities, Ann. Probab. 33 (2005) 1171-1178].

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Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 144 (2009)
Issue (Month): 5 (September)
Pages: 2146-2173

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Handle: RePEc:eee:jetheo:v:144:y:2009:i:5:p:2146-2173
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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  1. Massimo Marinacci & Paolo Ghirardato, 2001. "Risk, ambiguity, and the separation of utility and beliefs," ICER Working Papers - Applied Mathematics Series 21-2001, ICER - International Centre for Economic Research.
  2. F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
  3. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
  4. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  5. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  6. Massimo Marinacci, 2002. "Learning from ambiguous urns," Statistical Papers, Springer, vol. 43(1), pages 143-151, January.
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