基于Spartan随机场模型的空间连续性推断
On the Inference of Spatial Continuity using Spartan Random Field Models
摘要：
本文讨论了空间依赖的推理的背景下，最近提出的框架。更具体地说，本文着重研究了一类广义Gibbs随机场模型参数的估计，即，斯巴达空间随机场（SSRF）。参数推断的问题是基于距离度量的最小化。后者涉及样本约束（方差、广义"梯度“和"曲率”）与其整体对应物之间的专门设计的距离。度量的建设中使用的一般原则进行了讨论和直观的动机。为了能够从样本数据中计算度量，构造了广义“梯度”和“曲率”约束的估计器。这些估计，这并不限于SSRF，制定使用compatible支持的核函数。提出了一种直观的核带宽选择方法。在一定的正则性条件下，证明了可微随机场的估计量是渐近无偏的和相合的。对于连续但不可微的随机场，证明了估计量是渐近相合的。对于不同的核函数，显式地计算偏差。通过数值模拟研究了样本约束估计器的性能和SSRF的推理过程。
英文摘要：
This paper addresses the inference of spatial dependence in the context of a recently proposed framework. More specifically, the paper focuses on the estimation of model parameters for a class of generalized Gibbs random fields, i.e., Spartan Spatial Random Fields (SSRFs). The problem of parameter inference is based on the minimization of a distance metric. The latter involves a specifically designed distance between sample constraints (variance, generalized ``gradient'' and ``curvature'') and their ensemble counterparts. The general principles used in the construction of the metric are discussed and intuitively motivated. In order to enable calculation of the metric from sample data, estimators for generalized ``gradient'' and ``curvature'' constraints are constructed. These estimators, which are not restricted to SSRFs, are formulated using compactly supported kernel functions. An intuitive method for kernel bandwidth selection is proposed. It is proved that the estimators are asymptotically unbiased and consistent for differentiable random fields, under specified regularity conditions. For continuous but non-differentiable random fields, it is shown that the estimators are asymptotically consistent. The bias is calculated explicitly for different kernel functions. The performance of the sample constraint estimators and the SSRF inference process are investigated by means of numerical simulations.
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