Spatially adaptive Bayesian penalized splines with heteroscedastic errors
Spatially adaptive Bayesian penalized splines with heteroscedastic errors
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DOI：
10.1198/106186007x208768
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发表时间：
2007-06-01
影响因子：
2.4
通讯作者：
Goodner, Billy
中科院分区：
文献类型：
--
作者：
Crainiceanu, Ciprian M.;Ruppert, David;Goodner, Billy
惩罚样条已经成为一种越来越受欢迎的非参数平滑工具，因为它们使用低秩样条基，这使得计算易于处理，同时保持与平滑样条一样好的精度。本文扩展了惩罚样条方法的方差函数非参数化建模和使用空间自适应平滑参数。这种组合是令人满意的推理所必需的，并且可以通过贝叶斯MCMC有效地实现。控制空间自适应收缩的均值和异方差误差过程的方差过程建模为对数惩罚样条。我们讨论的先验和扩展的方法，特别是多元平滑的选择。完全贝叶斯方法提供了所有参数的联合后验分布，特别是误差标准差和惩罚函数。MATLAB，C和FORTRAN程序实现我们的方法是公开的。
Penalized splines have become an increasingly popular tool for nonparametric smoothing because of their use of low-rank spline bases, which makes computations tractable while maintaining accuracy as good as smoothing splines. This article extends penalized spline methodology by both modeling the variance function nonparametrically and using a spatially adaptive smoothing parameter. This combination is needed for satisfactory inference and can be implemented effectively by Bayesian MCMC. The variance process controlling the spatially adaptive shrinkage of the mean and the variance of the heteroscedastic error process are modeled as log-penalized splines. We discuss the choice of priors and extensions of the methodology, in particular, to multivariate smoothing. A fully Bayesian approach provides the joint posterior distribution of all parameters, in particular, of the error standard deviation and penalty functions. MATLAB, C, and FORTRAN programs implementing our methodology are publicly available.