Nonstationary Spatial Modeling for Multiple Point Sources, with Applications to Enviromnental Data

这项研究开发、评估和提供了方便的工具，用于实现由点源驱动的过程的参数建模。该项目使用分层贝叶斯方法对最近在模拟点源影响的背景下引入的过程分解模型进行扩展。过程分解模型将观察到的过程分解为趋势面、基线误差过程和可被视为对基线的冲击的附加误差过程(每个点源一个)。这种方法允许灵活和自主地对各个源进行建模。在评估预测不确定性时，贝叶斯方法很好地考虑了参数估计中的不确定性，很容易纳入先验信息，并且更灵活地根据多个点源的影响来分配等级。基于距离源邻域结构的马尔可夫随机场或条件自回归模型用于误差处理。权重的多变量分布描述了信源的相对等级。因为所有的模型都是参数的，所以很容易完成显著性检验。该项目实现了以下技术目标：a.测试几个点源的影响，在这些点源的确切位置已知的地方；b.根据影响对几个点源进行排名；c.提供可用于确定改变观察过程或优化设计过程的适当纠正行动的模型；d.通过考虑点源的影响，在未抽样的地点提供预测和预测不确定性的适当测量。该项目的教育部分包括向高中生传授所开发的方法的基础知识及其与环境公平等重大问题的相关性。1970年的《清洁空气法》及其1977年和1990年的修正案将污染源定义为“任何排放污染物的地方或对象。污染源可以是发电厂、工厂、干洗店、加油站或农场。汽车、卡车和其他机动车是污染源，工业中使用的消费品和机器也可以是污染源。”这些来源对人类健康的影响是有据可查的，对这些影响进行建模的重要性也是有据可查的。该项目通过开发、评估和提供方便的工具来对点源驱动的流程进行建模，从而满足了这种需求。由此产生的方法被应用于解决环境保护局对公众健康和福利的关注，即确定哪些氮氧化物(NOx)和二氧化硫(SO2)排放点对远离排放点的特定地点的环境浓度负有最大责任。这些特定地点的等级将有助于确定哪些排放地点需要更严格的法规来控制其在不同空间位置的影响。更广泛地说，项目成果可能会影响对点源的管理，将公平后果分配给生态或环境灾难附近的几个点源，并有助于确定适当的纠正行动。此外，针对高中生的教学模块的创建将提高这些学生在数学、物理和生物科学方面的学习准备。该项目由数学科学部的统计方案和MPS的多学科活动办公室共同支持。

This research develops, assesses, and provides convenient tools for implementing parametric modeling of processes that are driven by point sources. The project uses a hierarchical Bayesian approach to an extension of a process decomposition model that was recently introduced in the context of modeling the effect of point sources. The process decomposition model decomposes the observed process into a trend surface, a baseline error process, and additional error processes (one for each point source) that may be viewed as shocks to the baseline. This approach allows flexibility and autonomy to modeling the individual sources. The Bayesian approach properly accounts for uncertainty in parameter estimates when evaluating prediction uncertainty, easily incorporates prior information, and is more flexible for assigning ranks according to the impact of several point sources. A Markov random field or conditional autoregressive model based on a distance-to-source neighborhood structure is used for the error processes. A multivariate distribution of weights describes the relative ranks of the sources. Because all models are parametric, significance testing is easily accomplished. The project accomplishes the following technical goals: A. test the impact of several point sources, where exact locations of the point sources are known; B. rank several point sources according to impact; C. provide models that are useful for determining appropriate corrective action for altering an observed process or for optimizing a designed process; D. provide predictions, and appropriate measures of prediction uncertainties, at unsampled sites by accounting for the effects of point sources. The educational component of the project involves teaching high school students the rudiments of the methodology developed and its relevance to major issues such as environmental equity.The Clean Air Act of 1970 and its 1977 and 1990 amendments defined a pollution source as "any place or object from which pollutants are released. A source can be a power plant, factory, dry cleaning business, gas station or farm. Cars, trucks and other motor vehicles are sources, and consumer products and machines used in industry can be sources too." The effects of these sources on human health are well-documented, as is the importance of modeling these effects. This project responds to this need by developing, assessing, and providing convenient tools for modeling processes that are driven by point sources. The resulting methodology is applied to address a public health and welfare concern of the Environmental Protection Agency, namely to determine which nitrogen oxide (NOx) and sulfur dioxide (SO2) emission sites are most responsible for site-specific ambient concentrations far from the emission sites. These site-specific ranks will help determine which emission sites require stricter regulations for controlling their impact at different spatial locations. More generally, project results may impact the regulation of point sources, the assignment of equitable consequences to several point sources within the vicinity of an ecological or environmental disaster, and help in determining appropriate corrective actions. Furthermore, the creation of teaching modules aimed at high school students will improve the readiness of these students for studies in the mathematical, physical, and biological sciences. This project is jointly supported by the Statistics Program in the Division of Mathematical Sciences and the Office of Multidisciplinary Activities in MPS.