Foundations of neo-Bayesian statistics
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].
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Ghirardato, Paolo & Marinacci, Massimo, 2000. "Risk, Ambigity and the Separation of Utility and Beliefs," Working Papers 1085, California Institute of Technology, Division of the Humanities and Social Sciences.
- Paolo Ghirardato & Massimo Marinacci, 2000. "Risk, Ambiguity, and the Separation of Utility and Beliefs," Levine's Working Paper Archive 7616, David K. Levine.
- Paolo Ghirardato & Massimo Marinacci, 2000. "Risk, Ambiguity and the Separation of Utility and Beliefs," Econometric Society World Congress 2000 Contributed Papers 1143, Econometric Society.
- F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
- Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
- Schmeidler, David, 1989.
"Subjective Probability and Expected Utility without Additivity,"
Econometric Society, vol. 57(3), pages 571-87, May.
- David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
- Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
- Massimo Marinacci, 2002. "Learning from ambiguous urns," Statistical Papers, Springer, vol. 43(1), pages 143-151, January.
When requesting a correction, please mention this item's handle: RePEc:eee:jetheo:v:144:y:2009:i:5:p:2146-2173. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.