# On universal Bayesian adaptation

@article{Lember2007OnUB, title={On universal Bayesian adaptation}, author={J{\"u}ri Lember and Aad van der Vaart}, journal={Statistics and Risk Modeling}, year={2007}, volume={25}, pages={127-152} }

We consider estimating a probability density p based on a random sample from this density by a Bayesian approach. The prior is constructed in two steps, by first constructing priors on a collection of models each expressing a qualitative prior guess on the true density, and next combining these priors in an overall prior by attaching prior weights to the models. The purpose is to show that the posterior distribution contracts to the true distribution at a rate that is (nearly) equal to the rate…

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