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式。在过去十年中，可获得的实时地理信息量有所增加，确定性大气和海洋模型的精确度和分辨率也有所提高。在欧氏空间和球面上建立了一大类多元过程的时空模型，以解释不同变量之间的变异性和交叉依赖性。这类一般模型超越了标准假设，特别是平稳性。研究了所提出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。建议的框架和模型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被用来预报风车产生的能量，它们也是沿海海洋对风暴潮高度和沿海洪水程度等强风响应的数值预报的主要驱动力。这一研究项目最重要的科学贡献包括：引入了球面上灵活的空间模型，用于预测和估计地球表面更大区域上观察到的环境空间过程；一般情况下大空间时间点阵数据的似然逼近方法；空间点阵模型中引入条件相关概念的空间点阵多变量环境过程空间预测的通用和灵活模型；以及在大量观测数据和物理和化学模型存在的情况下，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和基于物理的数值模型。在过去十年中，现有的实时观测数量有所增加，在确定性化学、大气和海洋模型的精确度和分辨率方面也取得了进展。我们的方法将对潜在的感兴趣的时空过程提供更准确的表示和预测。通过我们的合作，我们将通过将这些方法应用于飓风风场、天气以及空气和土壤污染来改善天气和空气/土壤质量地图，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，以增进对数学和科学的理解。国际和平协会将在西班牙裔国家提供西班牙语短期课程，以扩大代表不足的地理和种族群体的参与。PI将教授一门高级空间统计方法课程，并将向学生介绍这里提出的新统计方法。调查人员将继续努力扩大少数群体和妇女对科学的参与，通过这个项目，PI将继续参与K-12教育努力，通过凯南课程和领导力发展方案和NCSU的科学之家。

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.