论文标题
空间随机过程的线性混合模型公式，具有可分离和产品-SUM协方差的计算进步
A Linear Mixed Model Formulation for Spatio-Temporal Random Processes with Computational Advances for the Separable and Product-Sum Covariances
论文作者
论文摘要
我们使用线性混合模型描述了时空随机过程。我们展示了多少个常用模型可以看作是该一般框架的特殊情况，并密切关注具有可分离或产品-AM协方差的模型。提出的线性混合模型配方促进了使用Stegle Eigendecompositions，Sherman-Morrison-Woodbury公式的递归应用以及Helmert-Wolf的递归应用以及Helmert-Wolf阻塞，以有效地反转可分离和产品 - 柔性的协方差矩阵，即使在每个空间位置都没有在每个时间点上观察到，也可以有效地倒置可分离和产品 - 摩托车，从而有助于实施新型算法。我们表明，我们的算法对标准Cholesky分解方法提供了明显的改进。通过模拟，我们评估了可分离和产品-SUM协方差的性能，并确定可分离协方差明显不如产品和协方差的情况。我们还比较了基于可能性的基于可能性的和半片状图的估计，并讨论两者的好处和缺点。我们使用建议的方法在2019年夏季分析美国俄勒冈州的每日最高温度数据。我们最终提供了基于观察到的数据属性的这些协方差和估计方法的指南。
We describe spatio-temporal random processes using linear mixed models. We show how many commonly used models can be viewed as special cases of this general framework and pay close attention to models with separable or product-sum covariances. The proposed linear mixed model formulation facilitates the implementation of a novel algorithm using Stegle eigendecompositions, a recursive application of the Sherman-Morrison-Woodbury formula, and Helmert-Wolf blocking to efficiently invert separable and product-sum covariance matrices, even when every spatial location is not observed at every time point. We show our algorithm provides noticeable improvements over the standard Cholesky decomposition approach. Via simulations, we assess the performance of the separable and product-sum covariances and identify scenarios where separable covariances are noticeably inferior to product-sum covariances. We also compare likelihood-based and semivariogram-based estimation and discuss benefits and drawbacks of both. We use the proposed approach to analyze daily maximum temperature data in Oregon, USA, during the 2019 summer. We end by offering guidelines for choosing among these covariances and estimation methods based on properties of observed data.
