基于广义平面旋转体模型的Gibbs Markov随机场空间数据建模
Spatial data modeling by means of Gibbs Markov random fields based on a generalized planar rotator model
摘要：
本文在广义平面旋转体（GPR）模型的基础上，引入了一种适用于笛卡尔网格上空间数据的Gibbs马尔可夫随机场。GPR模型概括了最近提出的修改后的平面旋转器（MPR）模型，包括在哈密顿额外的条款，更好地捕捉现实的空间数据，如平滑度，非高斯性和几何各向异性的功能。特别是，GPR模型包括高达无限数量的高阶谐波与指数消失的相互作用强度，方向依赖的最近的网格邻居，较长距离的邻居之间的相互作用，和两种类型的外部偏置场的双线性相互作用项。因此，与单参数MPR模型相比，GPR模型具有五个附加参数：高阶项的数量$n$和控制其衰减速率的参数$α$、交换各向异性参数$J^{nn}$、更远邻相互作用耦合$J^{fn}$和外场（偏置）参数$K$（或$K'$）。我们提出了各种合成数据的数值试验，展示了各自的条款对模型的预测性能的影响，我们讨论了这些结果与数据属性。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
