Experimental Design-based Weighted Sampling

随机抽样通常用于推断总体的感兴趣数量。本项目旨在开发一种确定性抽样技术，通过为每个样本引入权重来改进现有的抽样技术。基于数据压缩和子采样算法的最新发展，新的采样技术有可能克服现有技术所面临的计算挑战。所开发的技术是广泛的，可以在许多科学和工程领域中应用，例如不确定性量化，贝叶斯统计，模拟，随机优化，机器学习和数值分析，仅举几例。PI将开发软件包，免费向公众分发，以便广泛使用拟议的技术。采样技术还将在工业中实施，并在几个工程应用中进行测试，这将对社会产生广泛而直接的影响。该项目还为研究生提供研究培训机会。基于实验设计的加权抽样技术是通过研究统计学中的三大类问题而发展起来的：（1）不确定性量化，其中概率密度是已知的，并且是完全指定的，（2）贝叶斯计算，其中概率密度只知道比例常数，以及（3）数据压缩，其中概率分布是未知的。所提出的技术的关键思想是放松的限制，样本应该遵循的基本分布的人口。相反，最佳地生成样本以改善对感兴趣的量的估计，然后使用权重来校正分布失配。与现有的未加权样本相比，所得到的加权样本可以提供更鲁棒的性能。该项目开发了新技术，如最佳加权量化器，加权最小能量设计，自适应集成方法，使用顺序设计，加权孪生和监督数据压缩技术使用权重。总体而言，该项目将开发一套理论上合理和计算效率高的加权抽样技术，这代表了现有技术的重大进步，这些技术侧重于从目标分布中生成未加权样本。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。

Random sampling is commonly used for inferring quantities of interest of a population. This project aims to develop a deterministic sampling technique that improves upon the existing sampling techniques by introducing weights for each sample. Building on the recent developments of data compression and subsampling algorithms, the new sampling technique has the potential to overcome the computational challenges faced by the existing techniques. The developed techniques are broad and can have applications in many fields of science and engineering, such as uncertainty quantification, Bayesian statistics, simulation, stochastic optimization, machine learning, and numerical analysis, to name a few. The PI will develop software packages to be distributed to the public for free to enable the widespread use of the proposed techniques. The sampling techniques will also be implemented in industries and tested in several engineering applications, which will provide a broad and immediate impact on society. The project also provides research training opportunities for graduate students. The experimental design-based weighted sampling technique is developed by working on three broad classes of problems in statistics: (1) uncertainty quantification, where the probability density is known and fully specified, (2) Bayesian computation, where the probability density is known only up to a proportionality constant, and (3) data compression, where the probability distribution is unknown. The key idea of the proposed technique is to relax the restriction that the samples should follow the underlying distribution of the population. Instead, the samples are optimally generated to improve the estimation of the quantity of interest, and then weights are used for correcting the distributional mismatch. The resulting weighted sample can provide a more robust performance compared to the existing unweighted samples. The project develops new techniques such as optimally weighted quantizers, weighted minimum energy designs, adaptive integration methods using sequential designs, weighted twinning, and supervised data compression techniques using weights. Overall, this project will develop a suite of theoretically sound and computationally efficient techniques for weighted sampling that represents a significant advancement from the existing techniques that focus on generating unweighted samples from the target distribution.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.