Bayesian Adaptive Smoothing Splines Using
Bayesian Adaptive Smoothing Splines Using
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贝叶斯自适应平滑样条使用
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
F. Lindgren
中科院分区：
文献类型：
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作者：
Y. Yue;F. Lindgren
X抽象。光滑样条法是最流行的曲线设置方法之一，部分是因为经验证据支持它的有效性，部分是因为它优雅的数学公式。然而，在实际的统计工作中，有两个障碍限制了光滑样条法的应用。首先，由于基函数的数量大致等于样本大小，因此对于大数据集，它在计算上变得难以实现。其次，其全局平滑参数只能提供恒定的光滑量，这在估计非齐次函数时往往会导致较差的性能。在这项工作中，我们介绍了一类自适应光滑样条模型，它是通过用Nite元方法求解某些随机微分方程导出的。该方案将平滑参数扩展为连续的数据驱动函数，能够捕捉底层过程平滑程度的变化。新的模型是马尔可夫模型，这使得贝叶斯计算速度更快。仿真研究和实际数据算例验证了该方法的有效性。
x Abstract. The smoothing spline is one of the most popular curve-tting methods, partly because of empirical evidence supporting its eectiveness and partly because of its elegant mathematical formulation. However, there are two obstacles that restrict the use of the smoothing spline in practical statistical work. Firstly, it becomes computationally prohibitive for large data sets because the number of basis functions roughly equals the sample size. Secondly, its global smoothing parameter can only provide a constant amount of smoothing, which often results in poor performances when estimating inhomogeneous functions. In this work, we introduce a class of adaptive smoothing spline models that is derived by solving certain stochastic dierential equations with nite element methods. The solution extends the smoothing parameter to a continuous data-driven function, which is able to capture the change of the smoothness of the underlying process. The new model is Markovian, which makes Bayesian computation fast. A simulation study and real data example are presented to demonstrate the eectiveness of our method.