Posterior contraction rates for deconvolution of Dirichlet-Laplace mixtures

TL;DR

This paper establishes the rate at which Bayesian posterior distributions concentrate around the true mixing distribution and density in Dirichlet-Laplace mixture models, enhancing understanding of their statistical efficiency.

Contribution

It provides the first known contraction rates for the posterior in Dirichlet-Laplace mixture models under Wasserstein, Hellinger, and $L_q$ metrics.

Findings

Posterior contracts at a quantifiable rate in Wasserstein metric.

Contraction rates are established for the mixed density in Hellinger and $L_q$ metrics.

Results improve understanding of Bayesian nonparametric inference for 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.