Adaptive nonparametric Bayesian inference using location-scale mixture priors

TL;DR

This paper develops a flexible Bayesian framework using location-scale mixture priors, enabling adaptive nonparametric inference across various statistical tasks like regression, density estimation, and classification.

Contribution

It introduces a novel construction of kernel mixture priors that achieve rate-adaptive inference in nonparametric problems.

Findings

Achieves rate-adaptive inference with properly constructed priors

Uses Gaussian kernels with inverse gamma bandwidths and Gaussian weights

Applicable to multivariate regression, density estimation, and classification

Abstract

We study location-scale mixture priors for nonparametric statistical problems, including multivariate regression, density estimation and classification. We show that a rate-adaptive procedure can be obtained if the prior is properly constructed. In particular, we show that adaptation is achieved if a kernel mixture prior on a regression function is constructed using a Gaussian kernel, an inverse gamma bandwidth, and Gaussian mixing weights.