Bayesian Local Extrema Splines
Bayesian Local Extrema Splines
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贝叶斯局部极值样条
DOI：
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发表时间：
2016
期刊：
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通讯作者：
A. Herring
中科院分区：
文献类型：
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作者：
M. Wheeler;D. Dunson;A. Herring
考虑闭集X ？在R;其中假设函数在X内部不超过H个局部极值是合理的：根据贝叶斯方法，我们在一类新的局部极值样条上开发了非参数先验。这种方法在考虑的函数类中建模任何连续可微函数时被证明是一致的，并用于开发关于曲线形状的假设检验方法。开发了采样算法，并将该方法应用于对曲线形状感兴趣的仿真研究和数据示例中。
We consider the problem of shape restricted nonparametric regression on a closed set X ?in R; where it is reasonable to assume the function has no more than H local extrema interior to X: Following a Bayesian approach we develop a nonparametric prior over a novel class of local extrema splines. This approach is shown to be consistent when modeling any continuously differentiable function within the class of functions considered, and is used to develop methods for hypothesis testing on the shape of the curve. Sampling algorithms are developed, and the method is applied in simulation studies and data examples where the shape of the curve is of interest.