356 citations · 886 across the 6 of their papers we have counts for
6 papers
Frequentist coverage of adaptive nonparametric Bayesian credible sets
Botond Szabó, A. W. van der Vaart, J. H. van Zanten
We investigate the frequentist coverage of Bayesian credible sets in a nonparametric setting. We consider a scale of priors of varying regularity and choose the regularity by an em…
Adaptive nonparametric Bayesian inference using location-scale mixture priors
R. de Jonge, J. H. van Zanten
We study location-scale mixture priors for nonparametric statistical problems, including multivariate regression, density estimation and classification. We show that a rate-adaptiv…
Adaptive Bayesian estimation using a Gaussian random field with inverse Gamma bandwidth
A. W. van der Vaart, J. H. van Zanten
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 v…
Rates of contraction of posterior distributions based on Gaussian process priors
A. W. van der Vaart, J. H. van Zanten
We derive rates of contraction of posterior distributions on nonparametric or semiparametric models based on Gaussian processes. The rate of contraction is shown to depend on the p…
Reproducing kernel Hilbert spaces of Gaussian priors
A. W. van der Vaart, J. H. van Zanten
We review definitions and properties of reproducing kernel Hilbert spaces attached to Gaussian variables and processes, with a view to applications in nonparametric Bayesian statis…
Small Deviations of Smooth Stationary Gaussian Processes
F. Aurzada, I. A. Ibragimov, M. A. Lifshits +1
We investigate the small deviation probabilities of a class of very smooth stationary Gaussian processes playing an important role in Bayesian statistical inference. Our calculatio…