Adaptive nonparametric Bayesian inference using location-scale mixture priors
The Annals of Statistics · 2010 · Volume 38 · Issue 6
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.
Keywords
62C10, 62G08, 62G20, Adaptation, Bayesian inference, kernel mixture priors, Nonparametric regression, posterior distribution, rate of convergence
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