Development of Innovative Statistical Tools to Address Data-Analytic Challenges in Physics and Astronomy

天文学是高影响力统计挑战的沃土。我的新研究计划的总体目标是通过开发统计方法来推进天文学，这些方法结合了基于物理的计算机模拟器，适合手头的特定科学和数据分析挑战，并提供不确定性量化。这项工作涉及两个应用领域的四个目标。需要明确的是，拟议的计划旨在开发统计方法来应对天文学挑战，但不是物理学建议。在恒星活动的存在下寻找类地系外行星。天文学的一个重要目标是发现类地系外行星。一个复杂的问题是，大多数恒星都表现出活动（例如，星星斑点），可以模仿行星信号，并导致错误的检测。目标1是建立一个框架，用于探测围绕类太阳恒星运行的类地系外行星。这涉及开发一个模型选择程序，以确定具有最高系外行星探测能力的恒星活动模型，同时还使用机器学习来获得数据驱动的恒星活动代理，并提出灵活的统计模型来捕获它们。目标2调整框架，以适用于与太阳有很大不同的宿主恒星，使用分层模型来汇集类似恒星的信息，从而了解人口水平的恒星活动分布。计算机模型仿真与化学光谱校正。火星车上的ChemCam仪器获得化学光谱，以了解火星上岩石和土壤的成分。分解，即，确定目标的组成由于基质效应而变得复杂，基质效应是放大或抑制观察到的光谱中的峰的化合物之间的相互作用。目标3是将联合收割机计算机模拟器与ChemCam的光谱数据和贝叶斯变量选择技术相结合，以直接解决解聚问题。一个挑战是，一个多复合模拟器运行需要几个小时的现代并行计算平台。目标4旨在通过首先构建许多单复合模拟器的快速仿真器，然后使用分层模型将拟合仿真器与多复合模拟器的少量运行结合联合收割机来克服这种限制。数十亿美元用于开发外行星狩猎望远镜和火星探测器等仪器;理解和分析这些仪器生成的复杂数据集需要复杂的统计方法，而这是缺乏的。这项研究计划将为天文学家提供他们完成高影响力目标所需的工具，例如自信地探测类地系外行星或通过其地形组成探测火星的历史。该计划将支持高素质人员（HQP）的培训，为他们提供统计和机器学习方面的需求技能，并将普遍增加加拿大天体统计学研究的存在。

Astronomy is fertile ground for high-impact statistical challenges. The overarching goal of my new research program is to advance astronomy by developing statistical methods that incorporate physics-based computer simulators, are suited to the particular scientific and data-analytic challenges at hand, and provide uncertainty quantification. This effort involves four objectives in two application areas. To be clear, the proposed program aims to develop statistical methods to address astronomy challenges but is not a physics proposal. Hunting for Earth-like Exoplanets in the Presence of Stellar Activity. A prized goal in astronomy is the discovery of Earth-like exoplanets. A complication is that most stars exhibit activity (e.g., star spots) that can mimic a planetary signal and lead to false detections. Objective 1 is to develop a framework for detecting Earth-like exoplanets orbiting Sun-like stars. This involves developing a model selection procedure to identify stellar activity models with the highest exoplanet detection power, while also using machine learning to derive data-driven stellar activity proxies and proposing flexible statistical models to capture them. Objective 2 adapts the framework to apply to host stars that differ substantially from the Sun, using hierarchical models to pool information across similar stars and thereby learn population-level stellar activity distributions. Computer Model Emulation and Calibration with Chemical Spectra. The ChemCam instrument on the Curiosity Rover obtains chemical spectra to learn about the composition of rocks and soils on Mars. Disaggregation, i.e., determining the composition of a target, is complicated by matrix effects-interactions between chemical compounds that amplify or suppress peaks in the observed spectrum. Objective 3 is to combine computer simulators with ChemCam's spectral data and Bayesian variable selection techniques to directly solve the disaggregation problem. A challenge is that a multi-compound simulator run takes hours on modern parallel computing platforms. Objective 4 aims to overcome this limitation by first constructing fast emulators of many single-compound simulators, then using a hierarchical model to combine the fitted emulators with a few runs of the multi-compound simulator. Billions of dollars are spent developing instruments such as exoplanet-hunting telescopes and Mars rovers; comprehending and analyzing the complex datasets generated by these instruments requires sophisticated statistical methodology that is lacking. This research program will provide astronomers the tools they need to accomplish high-impact goals such as confidently detecting Earth-like exoplanets or probing the history of Mars via the composition of its terrain. The program will support the training of highly qualified personnel (HQP), providing them with in-demand skills in statistics and machine learning, and will generally grow the presence of astrostatistics research in Canada.