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

调查人员提出了统计科学三个领域的具体方法进步。 许多传统的统计方法在处理大规模数据集时会失效，因为它们的规模性不好--计算工作量或内存量随着问题的大小呈幂函数甚至指数级增长。 一个领域是计算机模拟模型输出的统计模拟。 在这里，研究人员建议自动生成自适应子设计，仔细选择和使用的数据，对每个特定的计算目标只承担的一小部分，并开发他们所谓的“并行部分仿真”，其中仿真是同时并行执行的一些模型输入保持在一个固定的值范围。 第二个领域是多尺度随机模型，利用无限可分的分布，一些模型功能，允许耦合并行分析在一个范围内的规模，与粗尺度需要更少的计算工作量和运行速度更快，以帮助更精细的尺度更快地达到平衡。 第三个领域是动态演化模型，其中计算工作集中在变化最快的方面，而其他方面则被视为缓慢变化或分段恒定。 所有的方法都适用于同一个重要的应用领域，火山事件的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，以解决在大量数据集的基础上进行原则性统计推断的问题。 这些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：改进与火山活动有关的风险定量评估方法。 在该应用领域，本研究的产品将是地图，指示哪些区域在指定时间长度（例如，1个月、1年、1十年）内面临指定的危险级别（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。 这些方法适用于现代经验科学的其他领域-既可以对其他地球物理灾害进行定量评估，也可以更广泛地对其他具有大量数据的科学工作进行定量评估。

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.