论文标题
基于广义平面旋转器模型的Gibbs Markov随机场的空间数据建模
Spatial data modeling by means of Gibbs Markov random fields based on a generalized planar rotator model
论文作者
论文摘要
我们介绍了基于广义平面旋转器（GPR）模型的笛卡尔网格的空间数据的Gibbs Markov随机字段。 GPR模型通过在哈密顿的附加术语中包括了更好地捕获空间数据的现实特征，例如平滑度，非陶氏和几何各向异性，从而概括了最近提出的改良平面旋转器（MPR）模型。特别是，GPR模型包括无限数量的高阶谐波，具有指数消失的相互作用强度，最近网格邻居之间双线性相互作用项的定向依赖性，更远距离的邻居相互作用以及两种类型的外部偏置场。 Hence, in contrast with the single-parameter MPR model, the GPR model features five additional parameters: the number $n$ of higher-order terms and the parameter $α$ controlling their decay rate, the exchange anisotropy parameter $J^{nn}$, the further-neighbor interaction coupling $J^{fn}$, and the external field (bias) parameters $K$ (or $K'$).我们介绍了各种合成数据的数值测试，这些数据证明了各个术语对模型预测性能的影响，并讨论了与数据属性有关的这些结果。
We introduce a Gibbs Markov random field for spatial data on Cartesian grids which is based on the generalized planar rotator (GPR) model. The GPR model generalizes the recently proposed modified planar rotator (MPR) model by including in the Hamiltonian additional terms that better capture realistic features of spatial data, such as smoothness, non-Gaussianity, and geometric anisotropy. In particular, the GPR model includes up to infinite number of higher-order harmonics with exponentially vanishing interaction strength, directional dependence of the bilinear interaction term between nearest grid neighbors, longer-distance neighbor interactions, and two types of an external bias field. Hence, in contrast with the single-parameter MPR model, the GPR model features five additional parameters: the number $n$ of higher-order terms and the parameter $α$ controlling their decay rate, the exchange anisotropy parameter $J^{nn}$, the further-neighbor interaction coupling $J^{fn}$, and the external field (bias) parameters $K$ (or $K'$). We present numerical tests on various synthetic data which demonstrate the effects of the respective terms on the model's prediction performance and we discuss these results in connection with the data properties.
