We introduce a method for statistically identifying the optimal locations of deep tubewells (dtws) to be installed in Matlab, Bangladesh. Dtw installations serve to mitigate exposure to naturally occurring arsenic found at groundwater depths less than 200 meters, a serious environmental health threat for the population of Bangladesh. We introduce an objective function, which incorporates both arsenic level and nearest town population size, to identify optimal locations for dtw placement. Assuming complete knowledge of the arsenic surface, we then demonstrate how minimizing the objective function over a domain favors dtws placed in areas with high arsenic values and close to largely populated regions. Given only a partial realization of the arsenic surface over a domain, we use a Bayesian spatial statistical model to predict the full arsenic surface and estimate the optimal dtw locations. The uncertainty associated with these estimated locations is correctly characterized as well. The new method is applied to a dataset from a village in Matlab and the estimated optimal locations are analyzed along with their respective 95% credible regions.

中文翻译：

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孟加拉Matlab最佳深管井位的贝叶斯空间设计

我们介绍了一种用于统计确定要安装在孟加拉国 Matlab 的深管井 (dtws) 最佳位置的方法。Dtw 装置用于减少暴露于地下水深度小于 200 米的天然砷，这是对孟加拉国人口的严重环境健康威胁。我们引入了一个目标函数，它结合了砷水平和最近的城镇人口规模，以确定 dtw 放置的最佳位置。假设对砷表面有完整的了解，然后我们演示了如何最小化域上的目标函数有利于将 dtws 放置在砷值高且靠近人口稠密地区的区域。给定域上砷表面的部分实现，我们使用贝叶斯空间统计模型来预测完整的砷表面并估计最佳 dtw 位置。与这些估计位置相关的不确定性也被正确表征。将新方法应用于 Matlab 中一个村庄的数据集，并分析估计的最佳位置及其各自 95% 的可信区域。