Scricciolo, Catia (2003) Adaptive posterior rate of convergence for infinite-dimensional exponential families. [Working Paper] WORKING PAPER SERIES, 25/2003 . , PADOVA
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The problem of estimating probability densities on the unit interval whose log-functions belong to a periodic Sobolev space is studied adopting a Bayesian approach. A prior is constructed so that the posterior converges at optimal rate in the minimax sense under Hellinger loss whichever is the degree of smoothness of the log-density. Thus, the point-wise posterior expectation of the density function provides an optimal non-parametric adaptive estimation procedure.
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