Computer-intensive Inference with Applications to Social Sciences

这个研究项目将开发新的统计计算机密集程序，以解决社会科学中的当前问题。两个不同的研究问题，是由共同的原则和方法将解决本研究。首先，该项目将开发新的方法，从排名数据中产生推论，而不依赖于强模型假设。从不同人群（如国家、学校或医院）获得的数据通常会按照某些绩效指标进行排序，比如以排名的形式从最好到最差。对排名数据的改进方法将在社会科学领域有许多应用，包括分析在阅读、数学和科学方面排名的国家，或根据代际收入流动性对社区进行排名。其次，该项目将解决“热手谬误”和人类对随机性的误解。对小样本条纹的普遍理解最近受到了挑战，本研究将提供可靠的统计工具来解决这一争议。此外，研究生将参与研究过程，该项目将开发免费且易于访问的软件。本项目中要处理的问题与共同的推理方法有关，这些方法将为需要正式统计分析的领域提供可靠的原则。因此，推理程序将不依赖于无法验证的基于模型的假设，计算机密集的统计推断方法将被使用，如重新抽样，自举和随机化方法。虽然机器计算将得到发展，但它们将伴随着证明其使用合理性的数学或理论结果。要解决的问题将需要新颖的见解，以便发展严格的统计性质，以便这些方法可以安全地应用于实践。此外，该项目将在多重测试和同时推理方面大量借鉴文献。例如，对秩的推断将导致构建具有保证误差控制的秩的同时置信区域。这将使研究人员知道经验排名是否代表了人口之间的真正差异，或者它们是否只是数据的人工制品。虽然要解决的问题源于具体的应用问题，但它们需要在统计学中具有根本重要性的解决办法。这些开放的问题不仅从数理统计的角度来看是令人兴奋和具有挑战性的，而且因为新兴的应用需要新的统计方法。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This research project will develop new statistical computer-intensive procedures that address current problems in the social sciences. Two different research questions that are related by common principles and methodologies will be addressed by this research. First, the project will develop new methods for generating inferences from ranked data that do not rely on strong model assumptions. It is common for data available from different populations (such as countries, schools, or hospitals) to be ordered by some performance measure, say from best to worst in the form of ranks. Improved methods for ranked data will have many applications in the social sciences, including the analysis of countries ranked in reading, math, and science or the ranking of neighborhoods by intergenerational income mobility. Second, the project will address the 'hot hand fallacy' and the human misperception of randomness. The common understanding of streaks in small samples has been challenged recently, and this research will provide solid statistical tools to address this controversy. In addition, graduate students will participate in the research process, and the project will develop free and easily accessible software.The problems to be addressed in this project are related by common inferential methodologies that will provide sound principles to areas in need of formal statistical analysis. So that inferential procedures will not rely on unverifiable model-based assumptions, computer-intensive methods of statistical inference will be used, such as resampling, bootstrap, and randomization methods. Although machine calculations will be developed, they will be accompanied by mathematical or theoretical results that justify their use. The problems to be addressed will require novel insights in order to develop rigorous statistical properties so that the methods may be applied safely in practice. In addition, the project will draw heavily on the literature in multiple testing and simultaneous inference. For example, inference for ranks will result in the construction of simultaneous confidence regions for ranks with guaranteed error control. This will allow researchers to know whether empirical rankings represent real differences between populations or whether they are just artifacts of the data. While the problems to be addressed stem from specific applied questions, they will require solutions that are of fundamental importance in statistics. These open problems are exciting and challenging not only from the point of view of mathematical statistics, but also because burgeoning applications demand new statistical methodology.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.