Posterior contraction rates for deconvolution of Dirichlet-Laplace mixtures

Abstract

We study nonparametric Bayesian inference with location mixtures of the Laplace density and a Dirichlet process prior on the mixing distribution. We derive a contraction rate of the corresponding posterior distribution, both for the mixing distribution relative to the Wasserstein metric and for the mixed density relative to the Hellinger and $L_q$ metrics.

19 pages. Minor revisions

References in corpus (4)

• Adaptive Bayesian multivariate density estimation with Dirichlet mixtures
• Posterior convergence rates of Dirichlet mixtures at smooth densities
• Convergence of latent mixing measures in finite and infinite mixture models
• Posterior concentration rates for empirical Bayes procedures, with applications to Dirichlet Process mixtures

Cited by in corpus (5)

• Nonparametric Bayesian Deconvolution of a Symmetric Unimodal Density
• Optimal Bayesian estimation of Gaussian mixtures with growing number of components
• Wasserstein convergence in Bayesian and frequentist deconvolution models
• Wasserstein convergence in Bayesian deconvolution models
• Sharp sup-norm Bayesian curve estimation