Entropy Bounds on Bayesian Learning

Gossner, Olivier; Tomala, Tristan

Gossner, Olivier; Tomala, Tristan (2008), Entropy Bounds on Bayesian Learning, Journal of Mathematical Economics, 44, 1, p. 24-32. http://dx.doi.org/10.1016/j.jmateco.2007.04.006

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Type

Article accepté pour publication ou publié

Date

2008

Journal name

Journal of Mathematical Economics

Volume

Number

Publisher

Elsevier

Pages

24-32

Abstract (EN)

An observer of a process View the MathML source believes the process is governed by Q whereas the true law is P. We bound the expected average distance between P(xt|x1,…,xt−1) and Q(xt|x1,…,xt−1) for t=1,…,n by a function of the relative entropy between the marginals of P and Q on the n first realizations. We apply this bound to the cost of learning in sequential decision problems and to the merging of Q to P.

Subjects / Keywords

Bayesian learning; Repeated decision problem; Value of information; Entropy

JEL

C11 - Bayesian Analysis: General