Geospatial referenced environmental data are extensively used in environmental assessment, prediction, and management. Data are commonly obtained by nonrandom surveys or monitoring networks, whereas spatial sampling and inference affect the accuracy of subsequent applications. Design-based and model-based procedures (DB and MB for short) both allow one to address the gap between statistical inference and spatial data. Creating independence by sampling implies that DB may neglect spatial autocorrelation (SAC) if the sampling interval is beyond the SAC range. In MB, however, a particular sampling design can be irrelevant for inferential results. Empirical studies further showed that MSE (mean squared error) values for both DB and MB are affected by SAC and spatial stratified heterogeneity (SSH). We propose a novel framework for integrating SAC and SSH into DB and MB. We do so by distinguishing the spatial population from the spatial sample. We show that spatial independence in a spatial population results in independence in a spatial sample, whereas SAC in a spatial population is reflected in a spatial sample if sampling distances are within the range of dependence; otherwise, SAC is absent in the spatial sample. Similarly, SSH in a population may or may not be inherited in data, and this depends on the sampling method. Thus, the population, sample, and inference constitute a so-called spatial statistic trinity (SST), providing a new framework for spatial statistics, including sampling and inference. This paper shows that it greatly simplifies the choice of method in spatial sampling and inferences. Two empirical examples and various citations illustrate the theory.

地理空间参考的环境数据广泛用于环境评估，预测和管理。数据通常是通过非随机调查或监视网络获得的，而空间采样和推断会影响后续应用程序的准确性。基于设计和基于模型的过程（简称DB和MB）都允许人们解决统计推断与空间数据之间的差距。通过采样创建独立性意味着，如果采样间隔超出SAC范围，则DB可能会忽略空间自相关（SAC）。但是，在MB中，特定的采样设计可能与推断结果无关。经验研究进一步表明，DB和MB的MSE（均方误差）值受SAC和空间分层异质性（SSH）的影响。我们提出了一个新颖的框架，用于将SAC和SSH集成到DB和MB中。我们通过将空间人口与空间样本区分开来做到这一点。我们表明，空间种群中的空间独立性导致空间样本中的独立性，而空间抽样中的SAC如果采样距离在依赖性范围内，则反映在空间样本中。否则，空间样本中不存在SAC。同样，总体中的SSH可能会或可能不会在数据中继承，这取决于采样方法。因此，总体，样本和推断构成了所谓的空间统计三位一体（SST），为空间统计（包括抽样和推断）提供了新的框架。本文表明，它极大地简化了空间采样和推断方法的选择。