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Abstract:
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We provide details of rates of convergence for posterior distributions in infinite dimensional models. This is achieved without the use of sieves, based on entropy measures, which have provided the basis for classical solutions and many recent Bayesian solutions. It turns out that a simple condition required for posterior consistency, which involves a finiteness of sums of square roots of prior probabilities, is all that is required for the rate of convergence to depend solely on how the prior concentrates about the correct sampling density. An optimal rate of convergence is obtained and examples presented.
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