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Empirical Distributions of Beliefs Under Imperfect Observation

Tomala, Tristan; Gossner, Olivier (2006), Empirical Distributions of Beliefs Under Imperfect Observation, Mathematics of Operations Research, 31, 1, p. 13-30. http://dx.doi.org/10.1287/moor.1050.0174

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Type
Article accepté pour publication ou publié
Date
2006
Journal name
Mathematics of Operations Research
Volume
31
Number
1
Publisher
Informs
Pages
13-30
Publication identifier
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Author(s)
Tomala, Tristan
Gossner, Olivier
Abstract (EN)
Let (xn)n be a process with values in a finite set X and law P, and let yn = f(xn) be a function of the process. At stage n, the conditional distribution pn = P(xn | x1,...,xn–1), element of {Pi} = {Delta}(X), is the belief that a perfect observer, who observes the process online, holds on its realization at stage n. A statistician observing the signals y1,...,yn holds a belief en = P(pn | x1,...,xn) isin {Delta}({Pi}) on the possible predictions of the perfect observer. Given X and f, we characterize the set of limits of expected empirical distributions of the process (en) when P ranges over all possible laws of (xn)n.
Subjects / Keywords
Stochastic process; signals; entropy; repeated games