Wavelet thresholding via a Bayesian approach
Wavelet thresholding via a Bayesian approach
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DOI：
10.1111/1467-9868.00151
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发表时间：
1998-01-01
影响因子：
5.8
通讯作者：
Silverman, BW
中科院分区：
文献类型：
--
作者：
Abramovich, F;Sapatinas, T;Silverman, BW
我们讨论了贝叶斯形式主义，它产生了一种类型的小波阈值估计在非参数回归。先验分布被施加到未知响应函数的小波系数上，旨在捕获大多数应用中常见的小波展开的稀疏性。对于事先指定的，后中值产生阈值化过程。我们的基础函数的先验模型可以进行调整，以给出落入任何特定Besov空间的函数。我们建立了先验模型的超参数和先验模型的实现所处的Besov空间的参数之间的关系。这样的关系给出了洞察的意义的Besov空间参数。此外，所建立的关系使得有可能在原则上将先验知识的函数的规律性属性的先验模型，其小波系数。然而，关于函数正则性的先验知识可能很难引出;考虑到这一点，我们提出了一个标准的先验超参数选择，在我们的例子中效果很好。仿真结果表明，该方法具有较好的鲁棒性和鲁棒性。我们还提出了一个应用程序的数据集，收集在麻醉学研究。
We discuss a Bayesian formalism which gives rise to a type of wavelet threshold estimation in nonparametric regression. A prior distribution is imposed on the wavelet coefficients of the unknown response function, designed to capture the sparseness of wavelet expansion that is common to most applications. For the prior specified, the posterior median yields a thresholding procedure. Our prior model for the underlying function can be adjusted to give functions falling in any specific Besov space. We establish a relationship between the hyperparameters of the prior model and the parameters of those Besov spaces within which realizations from the prior will fall. Such a relationship gives insight into the meaning of the Besov space parameters. Moreover, the relationship established makes it possible in principle to incorporate prior knowledge about the function's regularity properties into the prior model for its wavelet coefficients. However, prior knowledge about a function's regularity properties might be difficult to elicit; with this in mind, we propose a standard choice of prior hyperparameters that works well in our examples. Several simulated examples are used to illustrate our method, and comparisons are made with other thresholding methods. We also present an application to a data set that was collected in an anaesthesiological study.