标题： 非定态随机函数的空间变形模型估计 显示英文标题

标题： Estimation of Space Deformation Model for Non-stationary Random Functions

摘要： 平稳随机场已在地质统计学应用中成功使用了几十年。在某些情况下，假设整个感兴趣域内空间依赖结构是均匀的并不现实。一种用于建模和估计非平稳空间依赖结构的实际方法被考虑。该方法通过索引空间的双射连续变形，将一个非平稳随机场转化为平稳且各向同性的随机场。到目前为止，这种方法已经在多个独立实现的随机函数的数据背景下成功应用。在这项工作中，我们提出了一种在单次实现的情况下，利用空间变形进行非平稳地质统计学建模的方法，可能涉及不规则间隔的数据。该估计方法基于非平稳变差函数核估计器，用作地理空间中两个位置之间的差异度量。所提出的程序结合了核平滑、加权非度量多维标度和薄板样条径向基函数方面的内容。在模拟数据上，该方法能够恢复真实的变形。性能在合成数据和真实数据集上进行了评估。特别是，我们的方法优于平稳方法。除了预测外，所提出的方法还可以作为探索非平稳性的工具。 显示英文摘要

摘要： Stationary Random Functions have been successfully applied in geostatistical applications for decades. In some instances, the assumption of a homogeneous spatial dependence structure across the entire domain of interest is unrealistic. A practical approach for modelling and estimating non-stationary spatial dependence structure is considered. This consists in transforming a non-stationary Random Function into a stationary and isotropic one via a bijective continuous deformation of the index space. So far, this approach has been successfully applied in the context of data from several independent realizations of a Random Function. In this work, we propose an approach for non-stationary geostatistical modelling using space deformation in the context of a single realization with possibly irregularly spaced data. The estimation method is based on a non-stationary variogram kernel estimator which serves as a dissimilarity measure between two locations in the geographical space. The proposed procedure combines aspects of kernel smoothing, weighted non-metric multi-dimensional scaling and thin-plate spline radial basis functions. On a simulated data, the method is able to retrieve the true deformation. Performances are assessed on both synthetic and real datasets. It is shown in particular that our approach outperforms the stationary approach. Beyond the prediction, the proposed method can also serve as a tool for exploratory analysis of the non-stationarity.