Covariance Tapering for Likelihood-Based Estimation in Large Spatial Data Sets
Covariance Tapering for Likelihood-Based Estimation in Large Spatial Data Sets
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DOI：
10.1198/016214508000000959
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发表时间：
2008-12-01
影响因子：
3.7
通讯作者：
Nychka, Douglas W.
中科院分区：
文献类型：
--
作者：
Kaufman, Cari G.;Schervish, Mark J.;Nychka, Douglas W.
在基于高斯过程的空间模型中，极大似然法是一种很有吸引力的协方差参数估计方法。但是计算时，对于大型数据集，这种可能性在计算上是不可行的，对于具有观测值的数据集，需要O（m（3））计算。本文提出了协方差渐减的方法来近似这种情况下的可能性。在这种方法中。协方差矩阵是“锥形”的。“或逐元素乘以稀疏相关矩阵。由此产生的矩阵可以使用有效的稀疏矩阵算法进行操作。我们提出了两个近似高斯似然使用锥形。其中一个近似简单地用锥形版本替换模型协方差，而另一个近似则是由无偏估计方程理论驱动的。针对Matern类协方差函数的特殊情况，给出了估计量最大化锥化逼近的条件。像最大似然估计一样，强相合。此外，我们在模拟研究中表明，锥形估计可以有抽样密度非常相似的最大似然估计，即使锥形的程度是严重的。我们说明了在美国气象站的年总降水量异常的分析中的锥形方法的准确性和计算收益。
Maximum likelihood is an attractive method of estimating covariance parameters in spatial models based oil Gaussian processes. But calculating, the likelihood can he computationally infeasible for large data sets, requiring O(m(3)) calculations for a data set with a observations. This article proposes the method of covariance tapering to approximate the likelihood in this setting. In this approach. covariance matrixes are "tapered." or multiplied element wise by a sparse correlation matrix. The resulting matrixes can their be manipulated using efficient sparse matrix algorithms. We propose two approximations to the Gaussian likelihood using tapering. One of the approximations simply replaces the model covariance with a tapered version, whereas the other is motivated by the theory of unbiased estimating equations. Focusing on the particular case of the Matern class of covariance functions, we give conditions under which estimators maximizing the tapering approximations are. like the maximum likelihood estimator, Strongly consistent. Moreover, we show in a simulation study that the tapering estimators can have sampling densities quite similar to that of the maximum likelihood estimator even when the degree of tapering is severe. We illustrate the accuracy and computational gains of the tapering methods in an analysis of yearly total precipitation anomalies at weather stations in the United States.