Adaptive Bayesian Density Estimation in Lp-metrics with Pitman-Yor or Normalized Inverse-Gaussian Process Kernel Mixtures

Catia Scricciolo

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Adaptive Bayesian Density Estimation in Lp-metrics with Pitman-Yor or Normalized Inverse-Gaussian Process Kernel Mixtures

机译：具有Pitman-Yor或规范化逆高斯过程核混合物的Lp-metric中的自适应贝叶斯密度估计

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We consider Bayesian nonparametric density estimation using a Pitman-Yor or a normalized inverse-Gaussian process convolution kernel mixture as the prior distribution for a density. The procedure is studied from a frequentist perspective. Using the stick-breaking representation of the Pitman-Yor process and the finite-dimensional distributions of the normalized inverse-Gaussian process, we prove that, when the data are independent replicates from a density with analytic or Sobolev smoothness, the posterior distribution concentrates on shrinking Lp-norm balls around the sampling density at a minimax-optimal rate, up to a logarithmic factor. The resulting hierarchical Bayesian procedure, with a fixed prior, is adaptive to the unknown smoothness of the sampling density.

机译：我们将使用Pitman-Yor或归一化逆高斯过程卷积核混合物的贝叶斯非参数密度估计作为密度的先验分布。该程序是从常识性角度研究的。利用Pitman-Yor过程的破折表示和归一化高斯逆过程的有限维分布，我们证明，当数据是具有解析或Sobolev光滑度的密度的独立复制时，后验分布集中在将Lp范数球以最小最大最优速率围绕采样密度收缩，直至对数因子。具有固定先验的结果分层贝叶斯程序适用于未知的采样密度平滑度。

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《Bayesian Analysis》 |2014年第2期|共46页
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Catia Scricciolo;
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中图分类概率论与数理统计;
关键词
adaptationnonparametric density estimationnormalized inverseGaussian processPitman-Yor processposterior contraction ratesinc kernel;

机译：自适应非参数密度估计归一化逆高斯过程Pitman-Yor过程后收缩率inc;

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Adaptive Bayesian Density Estimation in Lp-metrics with Pitman-Yor or Normalized Inverse-Gaussian Process Kernel Mixtures

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