Bayesian Representation of Stochastic Processes under Learning: de Finetti Revisited
A probability distribution governing the evolution of a stochastic process has infinitely many Bayesian representations of the form mu = integral operator [subscript theta] mu[subscript theta] delta lambda (theta). Among these, a natural representation is one whose components (mu[subscript theta]'s) are 'learnable' (one can approximate mu[subscript theta] by conditioning mu on observation of the process) and 'sufficient for prediction' (mu[subscript theta]'s predictions are not aided by conditioning on observation of the process). The authors show the existence and uniqueness of such a representation under a suitable asymptotic mixing condition on the process. This representation can be obtained by conditioning on the tail-field of the process, and any learnable representation that is sufficient for prediction is asymptotically like the tail-field representation. This result is related to the celebrated de Finetti theorem, but with exchangeability weakened to an asymptotic mixing condition, and with his conclusion of a decomposition into i.i.d. component distributions weakened to components that are learnable and sufficient for prediction.
(This abstract was borrowed from another version of this item.)
|Date of creation:||May 1998|
|Date of revision:|
|Contact details of provider:|| Postal: |
Web page: http://www.kellogg.northwestern.edu/research/math/Email:
More information through EDIRC
|Order Information:|| Email: |
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.:
- Ehud Kalai & Ehud Lehrer, 1990.
"Rational Learning Leads to Nash Equilibrium,"
895, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- E. Kalai & E. Lehrer, 2010. "Rational Learning Leads to Nash Equilibrium," Levine's Working Paper Archive 529, David K. Levine.
- Ehud Kalai & Ehud Lehrer, 1990. "Rational Learning Leads to Nash Equilibrium," Discussion Papers 925, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Kalai, Ehud & Lehrer, Ehud, 1991. "Rational Learning Leads to Nash Equilibrium," Working Papers 91-18, C.V. Starr Center for Applied Economics, New York University.
- Ehud Kalai & Ehud Lehrer, 1992.
"Weak and Strong Merging of Opinions,"
983, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Lehrer, Ehud & Smorodinsky, Rann, 1997. "Repeated Large Games with Incomplete Information," Games and Economic Behavior, Elsevier, vol. 18(1), pages 116-134, January.
- Aumann, Robert J. & Heifetz, Aviad, 2002.
Handbook of Game Theory with Economic Applications,
in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 43, pages 1665-1686
- Dov Samet, 1996. "Looking Backwards, Looking Inwards: Priors and Introspection," Game Theory and Information 9610007, EconWPA.
- Kandori, M. & Mailath, G.J., 1991.
"Learning, Mutation, And Long Run Equilibria In Games,"
71, Princeton, Woodrow Wilson School - John M. Olin Program.
- Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
- M. Kandori & G. Mailath & R. Rob, 1999. "Learning, Mutation and Long Run Equilibria in Games," Levine's Working Paper Archive 500, David K. Levine.
- Jackson, Matthew O. & Kalai, Ehud, 1997.
"Social Learning in Recurring Games,"
Games and Economic Behavior,
Elsevier, vol. 21(1-2), pages 102-134, October.
- Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, vol. 9(2), pages 185-202, October.
- Dov Samet, 1996. "Common Priors and Markov Chains," Game Theory and Information 9610008, EconWPA.
When requesting a correction, please mention this item's handle: RePEc:nwu:cmsems:1228. 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: (Fran Walker)
If references are entirely missing, you can add them using this form.