Space and Space-Time Models for Large Datasets

在这个项目中，研究者主要关注高斯随机场的线性表示。他考虑的模型，要么避免显式计算的协方差矩阵或这样做相对较小的维度。所考虑过程的相关函数是非常一般的，避免了特殊的对称性或平稳性。PI考虑了在一般维度的域中工作的模型，特别是在球体上，用于网格化和非网格化数据。PI使用推理的分层方法来解释测量误差和不同的信息来源。他开发了统计上严格的程序，以减少时间序列的数量来总结动态演变随机场的信息，并设计了利用并行架构的快速Monte Carlo方法。研究人员研究了在大量位置和时间步长观察到的空间和时空过程的统计模型。PI的研究解决了对日益复杂的模型的需求，这些模型可以处理不同的信息来源，包括专家意见，并有效地处理几个不确定性来源。在大型数据集上运行时，PI模型考虑了时间演化动力学和空间异质性。这允许在全球范围内分析现象，充分利用最先进的推理和计算方法。一个例子的问题，其中统一的推论，从各种不同的气候模式是预测未来的气候是必要的。气候变化预测目前具有很大的社会影响。这项研究提供了工具，以提高我们的定量理解的不确定性，在这样的预测。这将提高决策者做出高质量决策的能力。

In this project the investigator focuses on linear representations ofGaussian random fields. He considers models that either avoid explicitcomputation of the covariance matrix or do so for relatively smalldimensions. The correlation functions of the considered processes arevery general, avoiding particular symmetries or stationarity. The PIconsiders models that work in domains of general dimension and, inparticular, on the sphere, for gridded and non-gridded data. The PI useshierarchical methods of inference to account for measurement errors anddifferent sources of information. He develops statistically rigorousprocedures to summarize the information of dynamically evolving randomfields in a reduced number of time series and designs fast Monte Carlomethods that take advantage of parallel architectures.The investigator studies statistical models for spatial andspatio-temporal processes observed at a large number of locations andtime steps. The PI's research addresses the need for increasinglysophisticated models that can deal with different sources ofinformation, include expert opinion and handle effectively severalsources of uncertainty. While operating on large datasets, the PI'smodels consider time evolving dynamics and spatial heterogeneity.This allows for the analysis of phenomena on global scales, making gooduse of state of the art inferential and computational methods. Anexample of a problem where unified inferences from a variety of datasources is needed is the prediction of future climate from differentclimate models. Climate change prediction currently has a large societalimpact. This research provides tools to enhance our quantitativeunderstanding of the uncertainties involved in such predictions. Thiswill improve the ability of decision makers to make quality policydecisions.