We clear land for agricultural purposes, we draw water from streams and aquifers, and we build houses in coastal regions for their ready access to the sea. Our need for food, water, and shelter is basic, but so is variability in our natural environment. Understanding this is key to the long-term sustainability of the anthropocene. At any location in the environment, long-term temporal averages may indicate regions that exceed sustainability thresholds. For example, environmental thresholds might be used by insurance companies to set the prices of insurance premiums. In this article, we present the problem of spatial-statistical inference on exceedance regions, defined as a set of locations whose long-term environmental condition is above a given threshold. An example is given of rainfall in Paraná, Brazil, averaged over a period of three decades.

我们清理土地用于农业目的，从溪流和含水层中抽水，并在沿海地区建造房屋以方便他们出海。我们对食物，水和住所的需求是基本的，但我们自然环境的变化也是如此。了解这一点是人类世代长期可持续性的关键。在环境中的任何位置，长期时间平均值都可能指示超出可持续性阈值的区域。例如，保险公司可能会使用环境阈值来设置保险费的价格。在本文中，我们提出了对超出区域的空间统计推断问题，这些区域被定义为长期环境条件高于给定阈值的一组位置。举一个例子，巴西巴拉那州的降雨平均为三个十年。