Functional Data Analysis for Synoptic Time-Domain Astronomy

宇宙现象表现出广泛的随时间变化的行为。直到最近，资源还十分有限，只有选定的种群才能在时间域中进行广泛监测，但现代望远镜和探测器可以比以前更快地测量宇宙体积。因此，天气学时间域天文学--研究大量人群的宇宙变异性--正在成为一种占主导地位的研究模式。这种调查不仅提供了更多的数据，而且提供了一种不同类型的数据，这需要一种新的统计学习方法，能够从大量多变量、不规则和非同步采样的光曲线集合中提取信息。天文学并不是面临这种数据性质变化的唯一学科。功能数据分析(FDA)是一个快速增长的统计学领域，它解决了从相关功能集合的样本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，从使用目录数据对变异性进行天体物理建模，到检测图像中的可变和瞬变源。一个主要的应用将是使用函数混合效应模型来分析周期变星的光曲线。特别是，造父变星是宇宙距离尺度的基础，人们希望这些新的功能模型能够提供更准确的亮度估计，从而放松对重要宇宙学参数如何准确测量的限制。其他适合FDA方法的问题包括微弱间歇信号的检测，以及根据光线曲线的特征对信号源进行分类。团队包括天文学和统计学方面的专家，并将在这两个学科进行创新研究。这项研究将通过直接合作，通过在两个社区传播结果，以及通过培训信息科学研究生解决天文学问题来加强他们的伙伴关系。所产生的方法将提高在天文测量中进行的大笔投资的科学回报。研究人员还参与了宾夕法尼亚州立大学面向天文学家的跨学科统计暑期学校，帮助年轻天文学家接受高级统计和机器学习方法方面的培训。

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.