论文标题
关于分数高斯田地的晶格近似值的有用性
On the usefulness of lattice approximations for fractional Gaussian fields
论文作者
论文摘要
分数高斯领域提供了丰富的空间模型，并且在多个科学分支中具有悠久的应用历史。但是，对小数田地的估计和推断提出了重大挑战。本书章节研究了在常规晶格上的分数拉普拉斯差异的使用，以近似于连续的分数高斯田地。重点是基于模型的地统计学和基于可能性的计算。对于一定范围的分数参数，我们证明了连续模型与其晶格近似之间存在相当大的一致性。对于该范围，可以从晶格近似中得出有关连续分数高斯磁场的参数估计和推断。有趣的是，常规的晶格近似有助于快速无基质计算，并启用各向异性表示。我们通过模拟研究和分析印度洋的海面温度来说明晶格近似的实用性。
Fractional Gaussian fields provide a rich class of spatial models and have a long history of applications in multiple branches of science. However, estimation and inference for fractional Gaussian fields present significant challenges. This book chapter investigates the use of the fractional Laplacian differencing on regular lattices to approximate to continuum fractional Gaussian fields. Emphasis is given on model based geostatistics and likelihood based computations. For a certain range of the fractional parameter, we demonstrate that there is considerable agreement between the continuum models and their lattice approximations. For that range, the parameter estimates and inferences about the continuum fractional Gaussian fields can be derived from the lattice approximations. Interestingly, regular lattice approximations facilitate fast matrix-free computations and enable anisotropic representations. We illustrate the usefulness of lattice approximations via simulation studies and by analyzing sea surface temperature on the Indian Ocean.
