Bayesian Smoothing with Gaussian Processes Using Fourier Basis Functions in the spectralGP Package.
Bayesian Smoothing with Gaussian Processes Using Fourier Basis Functions in the spectralGP Package.
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DOI：
10.18637/jss.v019.i02
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发表时间：
2007-04
影响因子：
5.8
通讯作者：
C. Paciorek
中科院分区：
文献类型：
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作者：
C. Paciorek
通过傅立叶基的平稳高斯过程的谱表示提供了用于各种统计模型的空间表面和非参数回归函数的计算高效的规范。我详细描述了这种表示，并介绍了R中用于计算的spectralGP包。由于大量的基础系数，某种形式的收缩是必要的，我专注于一个自然的贝叶斯方法，通过一个特定的参数化先验结构，近似平稳高斯过程在一个规则的网格。我回顾了几个模型，从文献中的数据，不躺在一个网格上，建议一个简单的模型修改，并提供示例代码演示MCMC采样使用spectralGP包。我描述了混合在某些情况下可能会很慢的原因，并提供了一些MCMC技术的建议，以改善混合，还提供了示例代码，以及一些基于经验的一般建议。
The spectral representation of stationary Gaussian processes via the Fourier basis provides a computationally efficient specification of spatial surfaces and nonparametric regression functions for use in various statistical models. I describe the representation in detail and introduce the spectralGP package in R for computations. Because of the large number of basis coefficients, some form of shrinkage is necessary; I focus on a natural Bayesian approach via a particular parameterized prior structure that approximates stationary Gaussian processes on a regular grid. I review several models from the literature for data that do not lie on a grid, suggest a simple model modification, and provide example code demonstrating MCMC sampling using the spectralGP package. I describe reasons that mixing can be slow in certain situations and provide some suggestions for MCMC techniques to improve mixing, also with example code, and some general recommendations grounded in experience.