Multi-Scale Models for Non-Stationary Spatial Datasets

这一研究项目将使用基于模型的方法开发空间数据的统计方法。位置参照观测的广泛可获得性导致需要对非常大的空间数据集合进行分析和预测。目前的空间数据模型难以处理大量不规则散布在空间中的观测数据。该项目将为大型数据集开发方法，这些数据集包含的表面在研究区域的某些部分变化性很小，但在该区域的其他部分变异性很高。将要开发的统计方法将适用于使用大型空间数据集的科学学科，包括定量环境科学、空间计量经济学和统计气候学。特别是，该项目将对从卫星观测到的基本气候变量的研究产生影响，如降水、积雪和野火。该项目还将为研究生提供教育和培训体验。将开发公开可用的软件。该研究项目将开发基于模型的非平稳空间场的地统计学方法，具有能够捕捉不同空间尺度上的变异性的多分辨率结构。分辨率随空间变化的事实增强了模型处理非平稳性的能力。为了实现对大数据集的可伸缩性，待开发的模型将通过使用紧支撑核和仔细定义的先验分布来引入稀疏性，该先验分布为多分辨率系数引入了强正则化。此外，本研究提出的模型拟合方法，通过将问题归结为变量选择和贝叶斯模型平均，避免了昂贵的跨维蒙特卡罗抽样。这个项目将探索两种模型拟合的方法。一种方法是通过随机搜索来估计非零系数。第二种方法涉及通过应用结合了关于域的递归划分的结构的信息的正则化项来估计最优模型的最大化策略。最初，该模型将针对高斯数据进行开发。稍后，它将扩展到指数分布家族中的观察。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This research project will develop statistical methods for spatial data using a model-based approach. The wide availability of location-referenced observations has resulted in a need to analyze and make predictions for very large collections of spatial data. Current models for spatial data have difficulties handling very large numbers of observations irregularly scattered in space. This project will develop methods for large datasets that contain surfaces with little variability in some parts of the region under study, but high variability in other parts of the region. The statistical methods to be developed will be applicable to the scientific disciplines that use large spatial datasets, including the quantitative environmental sciences, spatial econometrics, and statistical climatology. In particular, the project will have an impact on the study of essential climate variables that are observed from satellites, such as precipitation, snow cover, and wildfires. The project also will provide an educational and training experience for graduate students. Publicly available software will be developed.This research project will develop model-based geostatistical methods for non-stationary spatial fields, featuring a multi-resolution structure that is able to capture the variability at different spatial scales. The ability of the model to handle non-stationarity is enhanced by the fact that the resolution changes in space. To achieve scalability to large datasets, the model to be developed will induce sparseness by using compactly supported kernels, coupled with carefully defined prior distributions that introduce strong regularization for the multi-resolution coefficients. In addition, the model fitting approach developed in this research will avoid costly trans-dimensional Monte Carlo sampling by casting the problem as one of variable selection and Bayesian model averaging. This project will explore two approaches to model fitting. One approach consists of a stochastic search to estimate the non-zero coefficients. The second approach involves a maximization strategy to estimate the optimal model by applying a regularization term that incorporates information about the structure of a recursive partitioning of the domain. Initially, the model will be developed for Gaussian data. Later, it will be extended for observations in the exponential family of distributions.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.