Functional Data Analysis for Synoptic Time-Domain Astronomy

宇宙现象表现出广泛的时间依赖行为。 直到最近，资源仍然非常有限，只有选定的种群才能在时域中被广泛监测，但现代望远镜和探测器可以比以前更快地调查宇宙体积。 因此，天气时域天文学-在相当大的人群中研究宇宙变化-正在成为一种主要的研究模式。 这样的调查提供的不仅仅是更多的数据，而是一种不同类型的数据，需要一种新的方法来统计学习，能够从大量的多变量，不规则和异步采样的光变曲线中提取信息。 天文学并不是唯一一个面临数据性质变化的学科。 功能数据分析（FDA）是统计学中一个快速发展的领域，它解决了从对相关功能集合进行采样的数据集进行推断的问题。 目前的跨学科项目将使用FDA的概念和技术来开发新的方法，以解决调查数据分析的几个问题领域，从天体物理学建模的变化使用目录数据，以检测图像中的变量和瞬态源。 一个主要的应用将是使用函数混合效应模型分析周期变星的光变曲线。 特别是造父变星是宇宙距离尺度的基础，希望这些新的函数模型可以提供更准确的亮度估计，从而减轻对测量重要宇宙学参数的准确性的限制。 其他非常适合FDA方法的问题包括微弱间歇信号的检测，以及根据光源的光变曲线特征对其进行分类。该团队包括天文学和统计学专家，并将在这两个学科中进行创新研究。 这项研究将通过直接合作、在两个社区传播研究结果以及培训一名信息科学研究生从事天文学问题的工作来加强他们的伙伴关系。 所产生的方法将提高在天文调查中进行的大量投资的科学回报。 研究人员还参与了宾夕法尼亚州立大学的跨学科天文学家统计暑期学校，帮助培训年轻的天文学家掌握先进的统计学和机器学习方法。

Cosmic phenomena display a broad range of time-dependent behavior. Until recently, resources were sufficiently limited that only selected populations could be extensively monitored in the time domain, but modern telescopes and detectors can survey cosmic volumes much more quickly than before. As a consequence, synoptic time-domain astronomy - the study of cosmic variability across sizeable populations - is becoming a dominant mode of study. Such surveys provide not simply more data, but a different kind of data, requiring a new approach to statistical learning capable of extracting information from large ensembles of multivariate, irregularly and asynchronously sampled light curves. Astronomy is not the only discipline facing this change in the nature of data. Functional data analysis (FDA) is a rapidly growing area of statistics that addresses inference from datasets that sample ensembles of related functions. The present interdisciplinary project will use FDA concepts and techniques to develop new methods to address several problem areas of survey data analysis, from astrophysical modeling of variability using catalog data, to the detection of variable and transient sources in images. One main application will be the analysis of light curves of periodic variable stars using functional mixed effects models. In particular, Cepheid variable stars are a foundation of the cosmic distance scale, and the hope is that these new functional models can provide more accurate brightness estimates and therefore ease limits on how accurately important cosmological parameters can be measured. Other problems well suited to FDA methods include the detection of dim intermittent signals, and the classification of sources from features in their light curves.The team includes experts in astronomy and in statistics, and will pursue innovative research in both disciplines. This research will enhance their partnership by direct collaboration, by dissemination of results in both communities, and by training a graduate student in information sciences to work on problems in astronomy. The methods produced will improve the science return on the large investments being made in astronomical surveys. The investigators are also involved with the Penn State University's interdisciplinary Summer School in Statistics for Astronomers, helping to train young astronomers in advanced statistics and machine learning methods.