Anonymizing the GPS locations of observations can bias a spatial model's parameter estimates and attenuate spatial predictions when improperly accounted for, and is relevant in applications from public health to paleoseismology. In this work, we demonstrate that a newly introduced method for geostatistical modeling in the presence of anonymized point locations can be extended to account for more general kinds of positional uncertainty due to location anonymization, including both jittering (a form of random perturbations of GPS coordinates) and geomasking (reporting only the name of the area containing the true GPS coordinates). We further provide a numerical integration scheme that flexibly accounts for the positional uncertainty as well as spatial and covariate information. We apply the method to women's secondary education completion data in the 2018 Nigeria demographic and health survey (NDHS) containing jittered point locations, and the 2016 Nigeria multiple indicator cluster survey (NMICS) containing geomasked locations. We show that accounting for the positional uncertainty in the surveys can improve predictions in terms of their continuous rank probability score.

翻译：对观测点的GPS坐标进行匿名化处理，若处理不当，可能会导致空间模型的参数估计产生偏差，并削弱空间预测的准确性，这一问题在从公共卫生到古地震学等应用领域均具有重要影响。本研究证明，一种新提出的针对匿名化点位置进行地质统计建模的方法，可扩展至处理因位置匿名化导致的更一般类型的位置不确定性，包括随机扰动（即对GPS坐标进行随机抖动）和地理掩蔽（仅报告真实GPS坐标所在区域名称）。我们进一步提出了一种数值积分方案，该方案能灵活地考虑位置不确定性以及空间信息和协变量信息。我们将该方法应用于2018年尼日利亚人口与健康调查（NDHS）中（包含抖动点位置）的女性中学教育完成数据，以及2016年尼日利亚多指标类集调查（NMICS）中（包含地理掩蔽位置）的数据。研究结果表明，在调查中考虑位置不确定性，可以通过连续等级概率评分（CRPS）提升预测效果。