Spatial-temporal models and methods for big nonstationary multivariate

高维统计问题在环境科学中很普遍，特别是在土壤、大气和海洋数据应用中。在这些情况下，感兴趣的过程本质上是非线性和动态的。这些系统的不同信息来源包括空间观测数据以及基于物理和化学的数值模型。在过去十年中，可获得的实时地理信息的数量有所增加，确定性大气和海洋模式的复杂性和分辨率也有所提高。在欧几里得空间和球体上建立了一个广泛的时空模型，用于解释不同变量之间的可变性和交叉依赖性。这类模型超出了标准假设，特别是关于平稳性的假设。研究了所提方法的性质，以及估计的渐近性质。为了有效地实现所提出的统计模型，提出了海量空间数据的似然逼近方法。提出的框架和模型可用于更好地模拟土壤污染、空气污染和风场。这些高空间分辨率的风场用于预测风车产生的能量，它们也是沿海海洋对强风反应（如风暴潮高度和沿海洪水程度）的数值预报的主要强迫。目标是获得陆地和水上风场的更准确估计，以提高风暴潮预报和风能的质量。本研究项目最重要的科学贡献是：在地球上引入了灵活的空间模式，用于预测和估计在地球表面较大区域观测到的环境空间过程；一般情况下大时空点阵数据的似然逼近方法空间格上多元环境过程空间预测的通用和灵活模型，在空间格模型中引入了条件相关的概念；在观测和物理和化学模型中存在大量数据的空间预测和估计的先进方法。在这些情况下，感兴趣的过程本质上是非线性和动态的。这些系统的不同信息来源包括观测数据以及基于物理的数值模型。在过去十年中，可获得的实时观测量有所增加，确定性化学、大气和海洋模式的复杂性和分辨率也有所提高。我们的方法将提供更准确的表征和预测感兴趣的潜在时空过程。通过我们的合作工作，我们将通过将这些方法应用于飓风风场以及天气、空气和土壤污染，以改善天气和空气/土壤质量制图，从而帮助提高科学水平。研究人员将广泛传播这里提出的方法，以加强数学和科学的理解。PI将在西班牙国家开设西班牙语短期课程，以扩大代表性不足的地理和种族群体的参与。PI将教授高级空间统计方法的课程，并向学生介绍这里提出的新统计方法。研究人员将继续努力扩大少数民族和妇女在科学领域的参与，通过这个项目，PI将继续参与K-12教育工作，通过凯南课程和领导力发展项目研究员和NCSU科学之家。

High dimensional statistical problems are prevalent in the environmental sciences, particularly in soil, atmospheric, and oceanic data applications. In these cases the processes of interest are inherently nonlinear and dynamic. Different sources of information for these systems include spatial observational data as well as physics and chemistry based numerical models. Over the past decade there has been an increase in the amount of available real-time geographic information as well as advances in the sophistication and resolution of deterministic atmospheric and oceanic models. A broad class of spatial-temporal models is developed for multivariate processes on Euclidean spaces and the sphere to explain the variability and the cross-dependency between different variables. This general class of models goes beyond standard assumptions, in particular of stationarity. The properties of the proposed methods, as well as the asymptotic properties of the estimates are studied. Likelihood approximation methods for massive spatial data are presented to efficiently implement the proposed statistical models. The proposed framework and models are used to better model soil pollution, air pollution, and wind fields. These high spatial resolution wind fields are used to predict energy production from windmills, they are also the primary forcing for numerical forecasts of the coastal ocean response to force winds such as the height of the storm surge and the degree of coastal flooding. The goal is to obtain more accurate estimation of wind fields over land and water to improve the quality of storm surge forecasts, and wind energy.The most important scientific contributions of this research project are: the introduction of flexible spatial models on the sphere for prediction and estimation of environmental spatial processes observed over larger regions on the Earth's surface; methods for likelihood approximation of big spatial temporal lattice data in general situations; general and flexible models for spatial prediction of multivariate environmental processes on spatial lattices, introducing the concept of conditional correlation in spatial lattice models; and advanced methods for spatial prediction and estimation in the presence of massive data from observations and physical and chemistry models. In these cases the processes of interest are inherently nonlinear and dynamic. Different sources of information for these systems include observational data as well as physics-based numerical models. Over the past decade there has been an increase in the amount of available real-time observations as well as advances in the sophistication and resolution of deterministic chemistry, atmospheric and oceanic models. Our methodology will provide more accurate representation and prediction of the underlying space-time process of interest. Through our collaborative work, we will help the enhancement of science by implementing these methods to hurricane wind fields and to weather and air and soil pollution to improve weather and air/soil quality mapping. The investigators will disseminate broadly the methods proposed here to enhance mathematical and scientific understanding. The PI will offer short courses in Spanish in Hispanic countries to broaden the participation of underrepresented geographic and ethnic groups. A course in advanced spatial statistics methods will be taught by the PI, and the new statistical methods proposed here will be introduced to the students. The investigators will continue their efforts to broaden the participation of minorities and women in Sciences and the PI through this project will continue her involvement on K-12 educational efforts, through the Kenan Fellows for Curriculum and Leadership Development Program and the Science House at NCSU.