Collaborative Research: Adaptive Experimental Design for Astronomical Exploration

在大型项目中，天文学家通常会提出一个定义明确的问题，计划一系列观测，获取所有数据，然后进行分析。在观测资源稀缺和昂贵的情况下，根据迄今收集的数据选择要进行哪些观测的适应性办法，应该能够提高工作的准确性、精确度和效率。这项研究将开发一个基于迭代观测-推理-设计周期的灵活、自适应科学探索的通用框架，依赖于贝叶斯方法，称为贝叶斯自适应探索(BAE)。通过广泛的方法论研究发展BAE，然后将BAE应用于几个时变现象，将导致统计学上的许多理论和算法创新，并显著改进对太阳系外行星、双星系、太阳系中的小行星和附近星系中的变星的研究。由于计算要求极高，将探索几种方法，包括扩展现有的马尔可夫链蒙特卡罗和序贯蒙特卡罗推理算法，开发桥/路径重要性采样算法和高斯过程元模型，以及使用子区域自适应二次曲面。BAE是科学方法的自适应推广，因此将在许多学科中广泛应用。该项目将创建并广泛传播实施这些方法的公共领域软件，以及教程和教学材料。至少有一名研究生将接受广泛的跨学科培训。

AST-0507481ClydeIn large projects astronomers typically pose a well-defined question, plan a set of observations, take all the data, and then analyze it. When observational resources are scarce and expensive, an adaptive approach to selecting which observations to make, based on the data assembled thus far, should be able to improve the accuracy, precision and efficiency of the work. This research will develop a general framework for flexible, adaptive scientific exploration based on iterating an Observation-Inference-Design cycle, relying on Bayesian methods and called Bayesian Adaptive Exploration (BAE). Developing BAE through a broad range of methodological research, and then applying BAE to several time-variable phenomena, will lead to numerous theoretical and algorithmic innovations in statistics, and to significantly improved answers in the study of extra-solar planets, binary star systems, minor planets in our solar system, and variable stars in nearby galaxies. Since the required calculations are extremely demanding, several approaches will be explored, including extending existing Markov Chain Monte Carlo and sequential Monte Carlo inference algorithms, developing bridge/path importance sampling algorithms and Gaussian process meta-models, and the use of sub-region-adaptive quadrature.BAE is an adaptive generalization of the scientific method and will therefore be broadly applicable in many disciplines. This project will create and widely disseminate public-domain software implementing the methods, with tutorial and instructional material. At least one graduate student will receive extensive interdisciplinary training.