ITR DMS: Advancing the State of the Art in Statistical Computing and Simulation in Time Series

提出的工作是发展统计学和高性能计算（HPC）的新方法，并将其应用于伽马射线暴（GRB）时间剖面，以提取嵌入的信息，有助于我们理解这些爆炸事件。在统计学方面，本文将功能系数自回归（FCAR）模型扩展到一个多变量框架，并开发了FCAR模型的估计和推理方法。FCAR分析是高度计算密集型的，因此需要高性能计算（HPC）设施。由于FCAR分析技术适用于各种学科，因此开发的并行处理器计算工具足够灵活，可以用于环境建模或计量经济学等领域的其他问题。GRB数据的分析有两个主要目标。首先，将多元FCAR程序应用于GRB时间剖面，以确定(1)爆发期间时间尺度的演变，(2)爆发剖面的分类方案，以及(3)相对论性时间膨胀的证据，相对论性时间膨胀是一种有争议的效应，由于GRB性质的大动态范围而很微妙。第二个目标是应用核密度估计来查找和编目GRB计数光谱中的特征。此外，通过应用FCAR建模技术，以更一般的方式描述了光子光谱。从计算的角度来看，这些科学应用通常是大型的、数据并行的、不规则的和计算密集型的。高性能计算组件的重要贡献有两个方面。首先，开发了一种将动态调度集成到并行科学应用程序中的竞争性方法，该方法足够灵活，可以适应新兴技术，并且足够健壮，可以解决在并行和分布式环境中运行的实现的各种性能下降因素。在此基础上，结合先进的并行化技术和新颖的动态调度方法，构建了统计计算的软件基础结构。在这项工作中，主要研究人员开发了新的统计技术，用于分析随时间演变的复杂数据集。最重要的是隐藏在数据中的变量之间的关系，而这些关系往往不能用简单的数学函数来描述。一旦发现，这些关系就被用来描述潜在的物理因果现象，并预测未来的观察结果。在这个提议中使用的具体应用是研究伽马射线暴（GRB）的亮度和时间分布，GRB是每天在外层空间发生的极大的宇宙爆炸。随着更快更好的GRB余辉观测的出现，天体物理模型正变得越来越复杂。因此，为了分析时间概况，本研究开发了更复杂的统计工具，以揭示导致这些爆炸性事件的微妙线索。这项工作的结果有助于形成下一代GRB模型的基础。由于软件基础设施的开发使用了最先进的工具和技术，以及适应新兴技术的环境，因此计算挑战发挥了重要作用。

The work proposed is a blend of developing new methods in statistics and high performance computing (HPC), and their application to gamma-ray burst (GRB) time profiles to extract embedded information that could help with our understanding of these explosive events. In statistics, the proposed work extends functional coefficient autoregressive (FCAR) models to a multivariate framework and develops estimation and inference methods for FCAR models. FCAR analysis is highly computationally intensive, thus requiring the need for high performance computing (HPC) facilities. Since techniques in FCAR analyses are applicable to a wide variety of disciplines, the computational tools for parallel processors developed are flexible enough to be used in other problems in areas such as environmental modeling or econometrics. There are two principal goals for the analysis of the GRB data. First the multivariate FCAR procedures are applied to the GRB time profiles to determine (1) evolution of time scales during the burst, (2) classification schemes for burst profiles, and (3) evidence of relativistic time dilation, a debated effect that is subtle due to the large dynamic ranges in GRB properties. A secondary goal is the application of kernel density estimation to look for, and catalog, features in GRB count spectra. Additionally, the photon spectrum is described in a more general way by applying FCAR modeling techniques. From a computing perspective, these scientific applications are, in general, large, data-parallel, irregular and computationally intensive. The significant contribution of the HPC component is two-fold. First, a competitive methodology for integrating dynamic scheduling into parallel scientific applications is developed, which is flexible enough to adapt to new emerging technologies, and robust enough to address a wide spectrum of performance degradation factors of implementations running in parallel and distributed environments. Then from this methodology, a software infrastructure for statistical computing is built that integrates advanced parallelization techniques and novel dynamic scheduling methods. In this work, the principal investigators develop new statistical techniques for analysis of complex data sets which evolve over time. Of prime importance are the relationships between variables hidden in the data, and these cannot often be described by simple mathematical functions. Once discovered, these relationships are used to describe the underlying physical causal phenomena and to predict future observations. The specific application used in this proposal is the study of the brightness time profiles of gamma-ray bursts (GRB), extremely large cosmic explosions that occur daily in outer space. With the advent of quicker and better GRB afterglow observations, astrophysical models are becoming more sophisticated. Consequently, in order to analyze the time profiles, this study develops more sophisticated statistical tools to uncover subtle clues that indicate what causes these explosive events. The results of this work help form the foundation of the next generation of GRB models. The computing challenges play an essential role due to the development of a software infrastructure that uses state-of-the-art tools and techniques and environments that accommodate new emerging technologies.