Elements: A new generation of samplers for astronomy and physics

统计推断是科学数据分析的基础，通常由贝叶斯方法促进，贝叶斯方法通过蒙特卡洛抽样利用后验推断。传统上，这是一个计算挑战，在许多科学领域，包括但不限于天文学、宇宙学、晶格量子色动力学(QCD)和分子动力学，方法学往往构成最大的计算费用。幸运的是，近年来在抽样方法方面有了很大的学术进步，经常导致合成例子的计算量显著减少。该项目的主要目标是开发一个软件基础设施，以促进不同范围的科学家使用这些新的高效采样器。这项研究的结果预计将提供快速和准确的采样器，具有用户友好的界面。这些工具不仅限于在天文学和物理学中的应用，还可以广泛应用于各种科学和工程领域。此外，这些创新的方法可以被引入到统计推理发挥关键作用的课程中，包括数据科学和科学统计课程，从而进一步加强科学界对这些重要工具的学术和实践了解。该项目的技术努力涉及为两个尖端采样器开发软件基础设施，以促进不同科学领域的贝叶斯不确定性量化。第一个采样器PocoMC基于预条件蒙特卡罗算法，利用归一化流动和退火法进行快速准确的后验分析。第二个采样器，微正则哈密顿蒙特卡罗，使用基于梯度的方法，在非常高维的场景中有效，其中无梯度方法不足。与现有的替代方法相比，这两种采样器都显著降低了计算成本，为应用贝叶斯方法的科学家提供了潜在的标准工具。该项目的范围包括将这些新的采样器作为独立的包进行部署，并将其集成到几种广泛使用的概率编程语言中，最终旨在彻底改变科学和工程中使用的统计推断方法。这项由高级网络基础设施办公室颁发的奖项由天文科学部和数学和物理科学局内物理部信息前沿项目的物理学共同支持。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Statistical inference is fundamental to scientific data analysis, and is often facilitated by the Bayesian methodology, which leverages posterior inference via Monte Carlo sampling. Traditionally, this has been a computational challenge, with the methodology often constituting the largest computational expense in many scientific fields, including but not limited to astronomy, cosmology, lattice quantum chromodynamics (QCD), and molecular dynamics. Fortunately, recent years have witnessed considerable academic progress in sampling methods, often resulting in significant computational reductions on synthetic examples. The primary objective of this project is to develop a software infrastructure that facilitates the use of these new and efficient samplers by a diverse range of scientists. The outcome of this research is anticipated to provide speedy and precise samplers that boast a user-friendly interface. These tools are not limited to applications in astronomy and physics but can be applied broadly across various scientific and engineering fields. Additionally, these innovative methodologies can be introduced into the curriculum of courses where statistical inference plays a key role, including courses on Data Science and Statistics for Science, thereby further enhancing the academic and practical understanding of these vital tools in the scientific community.The technical endeavor of this project involves developing software infrastructure for two cutting-edge samplers to facilitate Bayesian uncertainty quantification in various scientific fields. The first sampler, PocoMC, based on the Preconditioned Monte Carlo algorithm, utilizes Normalizing Flows and annealing for swift and accurate posterior analysis. The second sampler, the MicroCanonical Hamiltonian Monte Carlo, employs gradient-based methods effective in very high-dimensional scenarios where gradient-free methods fall short. Both samplers offer significant computational cost reductions compared to existing alternatives, presenting themselves as potential standard tools for scientists applying Bayesian methods. The project's scope encompasses the deployment of these new samplers as standalone packages and their integration into several widely-used Probabilistic Programming Languages, ultimately aiming to revolutionize statistical inference methods used in science and engineering.This award by the Office of Advanced Cyberinfrastructure is jointly supported by the Division of Astronomical Sciences and the Physics at the Information Frontier program in the Division of Physics within the Directorate for Mathematical and Physical Sciences.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.