Heavy-tailed Bayesian nonparametric adaptation
重尾先验下的贝叶斯非参数自适应
We propose a new Bayesian strategy for adaptation to smoothness in nonparametric models based on heavy-tailed series priors. We illustrate it in a variety of settings, showing in particular that the corresponding Bayesian posterior distributions achieve adaptive rates of contraction in the minimax sense (up to logarithmic factors) without the need to sample hyperparameters. Unlike many existing procedures, where a form of direct model (or estimator) selection is performed,…