Estimation and Prediction in Spatial Models With Block Composite Likelihoods
Estimation and Prediction in Spatial Models With Block Composite Likelihoods
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DOI：
10.1080/10618600.2012.760460
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发表时间：
2014-06-01
影响因子：
2.4
通讯作者：
Niemi, Jarad
中科院分区：
文献类型：
--
作者：
Eidsvik, Jo;Shaby, Benjamin A.;Niemi, Jarad
本文提出了一种用于大型空间数据集估计和预测的分块合成似然方法。合成似然(CL)由相邻空间块对的联合密度构成。这允许将大数据集分成许多较小的数据集，每个数据集都可以单独评估，然后通过简单的求和进行组合。未知参数的估计是通过最大化块CL函数来获得的。此外，还提出了块CL下最优空间预测的一种新方法。参数估计和预测的渐近方差都是使用戈丹贝三明治矩阵计算的。该方法显著提高了计算效率，并且复合结构消除了一次将整个数据集加载到内存中的需要，完全避免了海量数据集对内存的限制。此外，通过使用并行计算来分配操作，可以进一步减少计算时间。模拟研究表明，CL估计和预测及其相应的渐近可信区间与基于全似然的估计和预测具有竞争性。在一个采矿业数据集和一个卫星检索数据集上演示了这一过程。实际数据实例表明，区块合成结果往往优于两个竞争对手：预测过程模型和固定秩克里格法。这篇文章的补充材料可以在该杂志的网站上在线获得。
This article develops a block composite likelihood for estimation and prediction in large spatial datasets. The composite likelihood (CL) is constructed from the joint densities of pairs of adjacent spatial blocks. This allows large datasets to be split into many smaller datasets, each of which can be evaluated separately, and combined through a simple summation. Estimates for unknown parameters are obtained by maximizing the block CL function. In addition, a new method for optimal spatial prediction under the block CL is presented. Asymptotic variances for both parameter estimates and predictions are computed using Godambe sandwich matrices. The approach considerably improves computational efficiency, and the composite structure obviates the need to load entire datasets into memory at once, completely avoiding memory limitations imposed by massive datasets. Moreover, computing time can be reduced even further by distributing the operations using parallel computing. A simulation study shows that CL estimates and predictions, as well as their corresponding asymptotic confidence intervals, are competitive with those based on the full likelihood. The procedure is demonstrated on one dataset from the mining industry and one dataset of satellite retrievals. The real-data examples show that the block composite results tend to outperform two competitors; the predictive process model and fixed-rank kriging. Supplementary materials for this article is available online on the journal web site.