Bayesian P-splines
Bayesian P-splines
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DOI：
10.1198/1061860043010
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发表时间：
2004-03-01
影响因子：
2.4
通讯作者：
Brezger, A
中科院分区：
文献类型：
--
作者：
Lang, S;Brezger, A
P-Spline是在加性和变系数模型框架内模拟协变量的非线性光滑效应的一种有吸引力的方法。在这篇文章中，我们首先开发了一个P-Spline的贝叶斯版本，并在第二步中以各种方式推广了该方法。首先，通过允许平滑参数的局部自适应来取代平滑参数恒定的假设。这在改变基本光滑函数的曲率或具有高度振荡的函数的情况下特别有用。在第二个扩展中，将一维P-Spline推广到二维曲面拟合，以模拟度量协变量之间的相互作用。在最后一步中，将该方法扩展到具有空间相关响应的情况，从而允许估计地质加性模型。推断完全是贝叶斯的，并使用最新的MCMC技术从后验数据中抽取随机样本。在几个仿真研究中，研究了贝叶斯P-样条的性能，并与文献中的其他方法进行了比较。我们通过慕尼黑公寓租金和人脑地形图的两个复杂应用来说明这一方法。
P-splines are an attractive approach for modeling nonlinear smooth effects of covariates within the additive and varying coefficient models framework. In this article, we first develop a Bayesian version for P-splines and generalize in a second step the approach in various ways. First, the assumption of constant smoothing parameters can be replaced by allowing the smoothing parameters to be locally adaptive. This is particularly useful in situations with changing curvature of the underlying smooth function or with highly oscillating functions. In a second extension, one-dimensional P-splines are generalized to two-dimensional surface fitting for modeling interactions between metrical covariates. In a last step, the approach is extended to situations with spatially correlated responses allowing the estimation of geoadditive models. Inference is fully Bayesian and uses recent MCMC techniques for drawing random samples from the posterior. In a couple of simulation studies the performance of Bayesian P-splines is studied and compared to other approaches in the literature. We illustrate the approach by two complex application on rents for flats in Munich and on human brain mapping.