论文标题
关于高斯Matérn随机字段中协方差参数的信息
On Information About Covariance Parameters in Gaussian Matérn Random Fields
论文作者
论文摘要
由于其描述不同平滑度行为的能力，因此协方差函数家族是当前用于分析地统计数据的最常用。但是，在许多应用中，平滑度参数设置为任意值。这种做法部分归因于试图估计所有协方差参数时面临的计算挑战，而部分是由于文献中的不合格的主张，表明地统计数据几乎没有有关平滑度参数的信息。这项工作对这一主张进行了批判性调查，并表明这是不正确的。具体来说，显示有关相关参数的数据的信息会取决于真实模型和采样设计，尤其是有关平滑度参数的信息可能很大，在某些情况下，有关范围参数的信息大。鉴于这些发现，我们建议重新评估上述实践，而是根据对范围和平滑度参数的基于数据的估计来确定推断，尤其是对于在不规则采样设计上观察到的强烈依赖的非平滑过程。每日降雨总数的数据集用于激励讨论并衡量这种常见做法。
The Matern family of covariance functions is currently the most commonly used for the analysis of geostatistical data due to its ability to describe different smoothness behaviors. Yet, in many applications the smoothness parameter is set at an arbitrary value. This practice is due partly to computational challenges faced when attempting to estimate all covariance parameters and partly to unqualified claims in the literature stating that geostatistical data have little or no information about the smoothness parameter. This work critically investigates this claim and shows it is not true in general. Specifically, it is shown that the information the data have about the correlation parameters varies substantially depending on the true model and sampling design and, in particular, the information about the smoothness parameter can be large, in some cases larger than the information about the range parameter. In light of these findings, we suggest to reassess the aforementioned practice and instead establish inferences from data-based estimates of both range and smoothness parameters, especially for strongly dependent non-smooth processes observed on irregular sampling designs. A data set of daily rainfall totals is used to motivate the discussion and gauge this common practice.
