论文标题
网络上的时空协方差模型，并在流上使用应用程序
Space-Time Covariance Models on Networks with An Application on Streams
论文作者
论文摘要
在时空域中定义的随机过程的二阶小规模依赖性结构是预测（或kriging）的关键。尽管已经致力于为空间域是有限维欧几里得空间或单位球体开发模型的巨大努力，但广义线性网络上的对应开发实际上是不存在的。为了填补这一空白，我们在广义线性网络上开发了广泛的参数，不可分割的时空协方差模型，然后与广义的gneing gneing gneiting类型的模型和1-合成的特征性功能在文献中以及量表混合物接近。我们提供了每类模型的示例，并研究了原点附近和无穷大的这些协方差函数的几何特征。我们还显示了欧几里得树上不同类别的时空协方差模型之间的联系。我们说明了不同方法在每日流温度数据集中构建的模型的使用，并通过交叉验证比较模型预测性能。
The second-order, small-scale dependence structure of a stochastic process defined in the space-time domain is key to prediction (or kriging). While great efforts have been dedicated to developing models for cases in which the spatial domain is either a finite-dimensional Euclidean space or a unit sphere, counterpart developments on a generalized linear network are practically non-existent. To fill this gap, we develop a broad range of parametric, non-separable space-time covariance models on generalized linear networks and then an important subgroup -- Euclidean trees by the space embedding technique -- in concert with the generalized Gneiting class of models and 1-symmetric characteristic functions in the literature, and the scale mixture approach. We give examples from each class of models and investigate the geometric features of these covariance functions near the origin and at infinity. We also show the linkage between different classes of space-time covariance models on Euclidean trees. We illustrate the use of models constructed by different methodologies on a daily stream temperature data set and compare model predictive performance by cross validation.
