In order to make spatial statistics computationally feasible, we need to forget about the covariance function
In order to make spatial statistics computationally feasible, we need to forget about the covariance function
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为了使空间统计在计算上可行，我们需要忘记协方差函数
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
H. Rue
中科院分区：
文献类型：
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作者：
Daniel P. Simpson;F. Lindgren;H. Rue
高斯随机场 (GRF) 是空间统计中结构化空间随机效应建模的最常见方法。不幸的是，它们的高计算成本使得直接使用 GRF 来解决大型问题是不切实际的，并且通常使用近似值。在本文中，我们比较了具有 Matérn 协方差函数的 GRF 的两种近似：核卷积近似和相关随机偏微分方程的高斯马尔可夫随机场表示。我们证明第二种方法是解决该问题的自然方法，并且比基于近似核卷积的方法更好。此外，我们表明，当随机场不平滑时，文献中描述的核方法不起作用。版权所有 © 2011 约翰·威利父子有限公司
Gaussian random fields (GRFs) are the most common way of modeling structured spatial random effects in spatial statistics. Unfortunately, their high computational cost renders the direct use of GRFs impractical for large problems and approximations are commonly used. In this paper, we compare two approximations to GRFs with Matérn covariance functions: the kernel convolution approximation and the Gaussian Markov random field representation of an associated stochastic partial differential equation. We show that the second approach is a natural way to tackle the problem and is better than methods based on approximating the kernel convolution. Furthermore, we show that kernel methods, as described in the literature, do not work when the random field is not smooth. Copyright © 2011 John Wiley & Sons, Ltd.