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On Bayesian Adaptation |
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| Authors: | Subhashis Ghosal Jüri Lember Aad van der Vaart |
| Affiliation: | (1) Department of Statistics, North Carolina State University, U.S.A.;(2) Eurandom, PO Box 51360, MB Eindhoven, The Netherlands;(3) Department of Mathematics, Vrije Universiteit Amsterdam, De Boelelaan 1081, Amsterdam, The Netherlands |
| Abstract: | We show that Bayes estimators of an unknown density can adapt to unknown smoothness of the density. We combine prior distributions on each element of a list of log spline density models of different levels of regularity with a prior on the regularity levels to obtain a prior on the union of the models in the list. If the true density of the observations belongs to the model with a given regularity, then the posterior distribution concentrates near this true density at the rate corresponding to this regularity. |
| Keywords: | posterior distribution rate of convergence adaptation sieves splines model selection |
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