GEOBEx: Geostatistical Binary Models For Extremes

评估污染、热浪、温度和洪水等环境问题的风险对生物多样性和人类健康至关重要。在许多情况下，这种对风险评估的需求可以很容易地转化为“是”或“否”的问题。例如，通过回答以下问题：特定污染物（如PM10）是否超过了高阈值？对于这些情况，一类被称为地质统计二元模型的数学模型可以帮助我们回答许多关于我们观察到的环境指数的问题，它们还可以帮助我们预测在我们没有观察到的地方出现高指数值。然而，拟合这些模型可能很困难，因为我们通常有一个不平衡的“是”和“否”的数量，这限制了信息量。本项目研究墨西哥城一种特定污染物（PM10）的水平。目标是开发一个结合创新统计模型和基于极值理论的高效贝叶斯分析方法的新框架。该框架旨在准确估计和预测特定地区随时间发生罕见二元极端事件的概率。

Assessing risks in environmental problems, such as contamination, heatwaves, temperature, and floods, is of utmost importance for biodiversity and human health. In many cases, this need for risk assessment can be easily translated into a ``yes" or ``no" problem. For example, by answering the question: does a specific pollutant, such as PM10, exceed a high threshold?For these cases, a class of mathematical models called geostatistical binary models can help us answer many questions regarding the environmental index we are observing, and they can also help us predict the occurrence of high index values in places where we do not observe it.However, fitting these models can be difficult since we usually have an imbalanced quantity of ``yes" and ``no", which limits the amount of information.This project studies the levels of a specific pollutant (PM10) in Mexico City. The goal is to develop a new framework that combines innovative statistical models and efficient Bayesian analysis methods based on extreme-value theory. This framework aims to accurately estimate and predict the probability of rare, binary extreme events in specific regions over time.