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

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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.