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Convergence and loss bounds for bayesian sequence prediction

2003
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IEEE Transactions on Information Theory
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The probability of observing x_t at time t, given past observations x_1...x_t-1 can be computed with Bayes' rule if the true generating distribution μ of the sequences x_1x_2x_3... is known. If μ is unknown, but known to belong to a class M one can base ones prediction on the Bayes mix ξ defined as a weighted sum of distributions ν∈ M. Various convergence results of the mixture posterior ξ_t to the true posterior μ_t are presented. In particular a new (elementary) derivation of the convergence

doi:10.1109/tit.2003.814488
fatcat:efwt2gyn25c3rj746gtquajjh4