# 地理统计

## 背景

Z(x)为特定位置x处的感兴趣变量的值。这个值是未知的（例如温度、降雨量、测压水位、地质相等）。尽管可以前往位置x测量该数值，但地统计学认为该值在尚未测量时是随机的。然而，Z(x)又不完全随机，可以用累积分布函数（CDF）定义，而该函数依赖于关于Z(x)值的某些已知信息（information）：

${\displaystyle F({\mathit {z}},\mathbf {x} )=\operatorname {Prob} \lbrace Z(\mathbf {x} )\leqslant {\mathit {z}}\mid {\text{information}}\rbrace .}$

1. 估计Z(x)的值，通常使用累积分布函数f(z,x)期望值中位數众数。其通常表现为估计问题。
2. 考虑每个位置上的每种可能结果，从整个概率密度函数f(z,x)采样。其方法通常是建立几个替代性的Z，称为实现（realization）。考虑在N维网格节点（或像素）中离散化的域。每个实现都是完整N联合分布函数的样本
${\displaystyle F(\mathbf {z} ,\mathbf {x} )=\operatorname {Prob} \lbrace Z(\mathbf {x} _{1})\leqslant z_{1},Z(\mathbf {x} _{2})\leqslant z_{2},...,Z(\mathbf {x} _{N})\leqslant z_{N}\rbrace .}$

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