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Empirical Distributions of Beliefs Under Imperfect Observation

Abstract : 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 = (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) () 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.
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Submitted on : Monday, May 31, 2010 - 4:05:40 PM
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Olivier Gossner, Tristan Tomala. Empirical Distributions of Beliefs Under Imperfect Observation. Mathematics of Operations Research, INFORMS, 2006, Vol.31,n°1, pp.13-30. ⟨10.1287/moor.1050.0174⟩. ⟨hal-00487960⟩

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