# Adaptive Bayesian estimation using a Gaussian random field with inverse Gamma bandwidth

@article{Vaart2009AdaptiveBE, title={Adaptive Bayesian estimation using a Gaussian random field with inverse Gamma bandwidth}, author={Aad W. Vaart and J. H. van Zanten}, journal={Annals of Statistics}, year={2009}, volume={37}, pages={2655-2675} }

We consider nonparametric Bayesian estimation inference using a rescaled smooth Gaussian field as a prior for a multidimensional function. The rescaling is achieved using a Gamma variable and the procedure can be viewed as choosing an inverse Gamma bandwidth. The procedure is studied from a frequentist perspective in three statistical settings involving replicated observations (density estimation, regression and classification). We prove that the resulting posterior distribution shrinks to the…

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