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，资源都非常有限，只能在时域内对选定的种群进行广泛监测，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——研究大规模人口中的宇宙变异性——正在成为一种主要的研究模式。这样的调查不仅提供了更多的数据，而且提供了一种不同的数据，需要一种新的统计学习方法，能够从多元、不规则和异步采样的光曲线的大集合中提取信息。天文学并不是唯一面临数据性质变化的学科。功能数据分析（FDA）是一个快速发展的统计学领域，它解决了从相关功能的样本集合的数据集推断的问题。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，从使用目录数据的变异性天体物理建模，到图像中变量和瞬态源的检测。一个主要的应用将是使用功能混合效应模型分析周期变星的光曲线。特别地，造父变星是宇宙距离尺度的基础，希望这些新的功能模型可以提供更准确的亮度估计，从而减轻对重要宇宙参数测量精度的限制。其他非常适合FDA方法的问题包括微弱间歇信号的检测，以及从其光曲线特征中对光源进行分类。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、通过在两个群体中传播结果以及通过培训一名信息科学研究生研究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跨学科的天文学家统计暑期学校，帮助培训年轻的天文学家掌握高级统计和机器学习方法。

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.