AI 中文总结
研究地质统计学中优先抽样问题，提出基于最近邻观测平均距离构建协变量的方法，经模拟研究和真实数据集验证，该方法能减少优先抽样影响，实现可靠推断并探讨了相关挑战与发展路径。
AI 中文摘要
在地质统计学中，通常假设采样位置是独立于潜在空间过程选择的。但在实际中，这一假设常被违反。例如在渔业中，采样点常被选来最大化预期捕获量，这在丰度过程和采样设计间产生随机依赖。这种优先抽样会引入大量偏差并影响统计推断。本研究探讨基于到最近邻观测的平均距离构建协变量以减轻优先抽样。将此协变量纳入地质统计模型可能能解释采样位置对空间变量的随机依赖。若能充分捕捉这种依赖，常规推断方法可无需借助更复杂模型。通过广泛模拟研究评估了所提方法，该研究探索了各种采样场景和空间配置。还用两个真实数据集展示了该方法的实际效用。结果表明纳入构造协变量能大幅减少优先抽样的影响，能用标准地质统计工具进行可靠推断。还讨论了实际挑战、局限及未来方法发展路径。
英文摘要
In geostatistics, it is commonly assumed that sampling locations are selected independently of the underlying spatial process. In practice, however, this assumption is frequently violated. In fisheries, for example, sampling sites are often chosen to maximize expected catches, creating a stochastic dependence between the abundance process and the sampling design. Such preferential sampling can introduce substantial bias and compromise statistical inference. This study investigates the use of constructed covariates, based on average distances from nearest neighbours observations, that are able to mitigate preferential sampling. The inclusion of such covariate in the geostatistical model might be able to account for the stochastic dependence of sampling locations on the spatial variable. If this inclusion sufficiently captures the dependence, conventional methods of inference may be applied without resorting to more complex models. The proposed methodology is evaluated through an extensive simulation study that explores a variety of sampling scenarios and spatial configurations. Additionally, we demonstrate the practical utility of the approach using two real-world datasets: one on fishery landings provided by the Instituto Português do Mar e da Atmosfera, and another concerning lead pollution biomonitoring in Galicia. Results show that incorporating the constructed covariate can substantially reduce the impact of preferential sampling, enabling reliable inference with standard geostatistical tools. We also discuss practical challenges, limitations, and paths for future methodological development.
