Collaborative Research: Statistical and Computational Models and Methods for Extracting Knowledge from Massive Disparate Data for Quantifying Uncertain Hazards

研究人员在统计科学的三个领域提出了具体的方法学进展。许多传统的统计方法不适用于海量数据集，因为它们不能很好地扩展-计算工作量或内存量以幂函数形式增加，甚至随着问题大小的增加而指数增加。其中一个领域是对计算机模拟模型的输出进行统计模拟。在这里，研究人员建议自动生成自适应子设计，仔细选择并仅使用与每个特定计算目标有关的数据的一小部分；并开发他们所称的“并行部分仿真”，即在某些模型输入保持在固定值范围内的同时进行仿真。第二个领域是多尺度随机模型，利用某些模型特征的无限可分分布来允许在一系列尺度上进行耦合并行分析，其中较粗的尺度需要较少的计算工作量并且运行得更快，以帮助较细的尺度更快地达到平衡。第三个领域是动态演化模型，其中计算精力集中在变化最快的方面，而其他方面被视为缓慢变化或分段恒定。所有的方法都应用于同一个重要的应用领域，即火山事件地球物理灾害的定量评估。研究人员建议开发新的数学、统计和计算方法，以解决在海量数据集基础上进行原则性统计推断的问题。新方法是在一个具体的重要社会问题的背景下开发和应用的：改进火山活动相关风险的量化评估方法。在这一应用领域，这项研究的产品将是地图，指出哪些地区在指定的时间长度(例如，1个月、1年、10年)内面临特定级别的危险(例如，1000：1、100：1、10：1)，并根据地球物理证据和经过验证的计算模型进行估计。这些方法也适用于现代经验科学的其他领域-无论是对其他地球物理灾害进行定量评估，还是更广泛地说，用于其他具有大量数据的科学努力。

The investigators propose specific methodological advances in three areas of statistical science. Many conventional statistical methods break down for massive data sets because they do not scale well--- the amount of computational effort or memory increases as a power or even exponentially with problem size. One area is that of statistical emulation of the output of computer simulation models. Here the investigators propose to generate adaptive subdesigns automatically, carefully selecting and using only the small subset of the data that bears on each specific computational goal; and to develop what they call "parallel partial emulation" in which emulation is performed simultaneously in parallel with some model inputs kept at a range of fixed values. A second area is that of multiple scale stochastic models, exploiting infinitely-divisible distributions for some model features to permit coupled parallel analyses at a range of scales, with coarser scales requiring less computational effort and running faster to help the finer scales reach equilibrium faster. A third area is dynamic evolution models in which computational effort is focused on those aspects that change most rapidly, while other aspects are treated as slowly-varying or piecewise-constant. All methods are applied to the same important application area, the quantitative assessment of geophysical hazard for volcanic events.The investigators propose to develop new mathematical, statistical, and computational methods to address the problem of making principled statistical inference on the basis of massive data sets. The new methods are developed and applied in the context of a specific important societal problem: improving methods for the quantitative assessment of risk associated with volcanic activity. In this application area the product of this research would be maps indicating which areas face specified levels of hazard (say, 1000:1, 100:1, 10:1) for specified lengths of time (say, 1 month, 1 year, 1 decade), with estimates based on geophysical evidence and validated computational models. The methods are applicable in other areas of modern empirical science--- both for making quantitative assessments of other geophysical hazards and, more broadly, other scientific endeavors with large amounts of data.