Full adaptation to smoothness using randomly truncated series priors with Gaussian coefficients and inverse gamma scaling

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• 作者：Jan van Waaij ; ^{j.vanwaaij@uva.nl} ; Harry van Zanten ^{hvzanten@uva.nl}
• 关键词：Posterior convergence ; Adaptation ; Series prior ; Bayesian nonparametric statistics
• 刊名：Statistics & Probability Letters
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：123
• 期：Complete
• 页码：93-99
• 全文大小：418 K
• 卷排序：123

文摘

We study random series priors for estimating a functional parameter f∈L2[0,1]f∈L2[0,1]. We show that with a series prior with random truncation, Gaussian coefficients, and inverse gamma multiplicative scaling, it is possible to achieve posterior contraction at optimal rates and adaptation to arbitrary degrees of smoothness. We present general results that can be combined with existing rate of contraction results for various nonparametric estimation problems. We give concrete examples for signal estimation in white noise and drift estimation for a one-dimensional SDE.