Statistics for Stars and Galaxies: techniques for non-parametric time series analysis and Bayesian inference in astronomy

天文学中的观测数据不同于实验数据，因为我们不能进行重复的实验;虽然我们可以选择在天空中观察哪些物体，使用哪些望远镜，但最终宇宙为我们提供了一个样本。因此，我们采用的统计方法对于正确解释这些数据至关重要。天体统计学是一个相对较新的跨学科领域，位于天文学和统计学的界面，并寻求在这两个领域创造新的知识。通过天体统计学，我们可以回答有关宇宙的科学问题，同时为空间和时间域中复杂的噪声数据发现新的统计方法。过去十年，美国和英国都出现了跨学科的天体统计学研究小组。作为多伦多大学的新教师，以及天文学与天体物理学系（DoAA，51%）和统计科学系（DoSS，49%）之间的联合任命，我处于独特的地位，领导加拿大第一个天体统计学研究项目。我设想一个多元化的天体统计学研究团队（ART）由DoAA和DoSS的本科生，研究生和博士后研究人员组成，他们不仅对统计学领域做出贡献，而且还在天文学领域做出突破性的发现。通过我们的研究，艺术将培养高素质的人才与抢手的定量，技术和定性技能。该研究计划的长期目标是：（1）开发新的统计方法和模型比较技术，用于研究银河系，银河系恒星隆起和球状星团（GC）的质量分布;（2）严格测试，验证和建立一种新的非参数时间序列分析技术，用于研究恒星的时间变化。有趣的统计挑战，以克服在这两条线的研究是，数据是不完整的，并受到显着的测量不确定性，以及物理模型是非线性的。我们的研究将帮助我们回答有关宇宙中大小系统的科学问题，从而推进有关暗物质，星系演化和恒星演化的知识。此外，新的统计方法和技术将推动统计领域的发展，并在进行贝叶斯推理和时间序列分析的其他学科中具有广泛的应用。考虑到这一点，ART的研究将是可复制的和开源的，以便更广泛的科学界可以从我们的努力中受益。该计划还将帮助我们为21世纪20年代的大数据发布做好准备，包括来自大型光谱巡天望远镜（LSST）的超过60 TB的时间序列数据，这些数据将彻底改变时域天文学领域。

Observational data in astronomy are different from experimental data because we cannot perform repeated experiments; although we can choose which objects to observe in the sky and which telescopes to use, ultimately the universe provides us with one sample. Thus, the statistical methods we employ are critical to the proper interpretation of these data. Astrostatistics is a relatively new interdisciplinary field that resides at the interface of astronomy and statistics and that seeks to create new knowledge in both fields. With astrostatistics, we can answer scientific questions about the universe while simultaneously discovering new statistical approaches for complicated, noisy data in the spatial and time domains. Interdisciplinary astrostatistics research groups have cropped up in both the United States and the UK in the past ten years. As new faculty at the University of Toronto, and jointly appointed between the Department of Astronomy & Astrophysics (DoAA, 51%) and the Department of Statistical Sciences (DoSS, 49%), I am in the unique position to lead the first astrostatistics research program in Canada. I envision a diverse Astrostatistics Research Team (ART) comprised of DoAA and DoSS undergraduate students, graduate students, and postdoctoral researchers who not only make contributions to the field of statistics but who also make groundbreaking discoveries in the field of astronomy. Through our research, the ART will train highly-qualified personnel with sought-after quantitative, technical, and qualitative skills. The long-term objectives of this research program are to (1) develop new statistical methods and model comparison techniques for studying the mass distribution of the Milky Way Galaxy, the Galactic Stellar Bulge, and Globular Clusters (GCs), and (2) rigorously test, validate, and build upon a new non-parametric time series analysis technique for studying the time-variability in stars. The interesting statistical challenges to overcome in both lines of research are that the data are incomplete and subject to significant measurement uncertainty, and that the physical models are non-linear. Our research will help us answer scientific questions about large and small systems in the universe, thereby advancing knowledge about dark matter, galactic evolution, and stellar evolution. Moreover, the new statistical methodologies and techniques will advance the field of statistics and have broad applications in other disciplines that perform Bayesian inference and time series analysis. With this in mind, the ART's research will be reproducible and open-source, so that the broader scientific community can benefit from our efforts. This program will also help prepare us for big data releases in the 2020s, including over 60TB of time series data from the Large Spectroscopic Survey Telescope (LSST) that will revolutionize the field of time-domain astronomy.