Hybrid Methods for Statistical and Econometric Modeling

这个研究项目将开发统计方法来解释一个不可避免的事实，即大多数模型只代表现实的近似值，研究人员经常面临许多不同的可信模型的选择。该项目将从三个方面解决这一问题：(i)对经济学和统计学中广泛使用的矩法方法进行修改，以解释不完美的测量数据；（ii）提供正式的统计方法，以解释研究人员通常根据他们拥有的数据量调整模型的复杂性；（iii）通过开发预测方法，将多个（可能不完美的）模型的预测结合起来，以产生更稳健的预测。为了实现这一目标，在非常不同的研究领域开发的技术将被结合和增强，并且它们在与最初设想的环境非常不同的环境中的优势将被利用。要开发的方法通常可以应用于使用统计建模的许多研究领域，因此可以影响医学，天气预报，流行病演变预测，气候建模或社会干预计划有效性评估等不同领域。研究生将参与研究过程，实现新方法的计算机程序将向公众开放。本研究项目将解决在数据拒绝模型时为矩量方法分配逻辑解释的问题。这个问题将通过确定在数据和模型之间达成一致所需的最小测量误差来解决。这种方法将借鉴两个目前非常活跃的研究领域，即经验可能性和最佳运输。该项目的另一部分将为研究人员提供方法，在利用非标准推断的一般领域的技术进行统计推断时，解释他们的模型选择过程。最后，该项目将利用一个很大程度上被忽视的事实，即多模型预测过程可以写成一个模型选择问题，其中模型选择变量可以设置值，从而强调与近年来受到相当关注的所谓集识别模型的联系。该研究将为多模型预测中常用的贝叶斯方法提供一个自然频率对应。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 statistical methods that account for the unavoidable fact that most models only represent approximations to reality, and researchers often are faced with a choice of a number of different plausible models. The project will tackle this issue along three fronts: (i) by devising a modification to the widely used method-of-moment approaches from economics and statistics that account for imperfectly measured data, (ii) by providing formal statistical methods that account for the fact that researchers typically adapt the complexity of their model based on the amount of data they have, and (iii) by developing forecasting methods that combine the predictions of multiple (possibly imperfect) models to yield more robust forecasts. To accomplish this, techniques developed in very diverse fields of study will be combined and augmented, and their advantages in contexts very different from where they initially were conceived will be leveraged. The methods to be developed generally can be applied in many areas of study that employ statistical modeling and thus could impact fields as diverse as medicine, weather forecasting, pandemic evolution predictions, climate modeling, or the evaluation of the effectiveness of social intervention programs. Graduate students will be involved in the research process, and computer programs implementing the new methods will be made publicly available.This research project will solve the problem of assigning a logical interpretation to the method of moments when the data rejects the model. The problem will be addressed by determining the minimum amount of measurement error that would be needed to reach agreement between the data and the model. This approach will draw from two currently very active areas of research, namely, empirical likelihood and optimal transport. Another part of the project will provide researchers with methods to account for their model selection process when making statistical inference by leveraging techniques from the general field of nonstandard inference. Finally, the project will exploit the largely overlooked fact that a multi-model forecasting process can be written as a model selection problem, where the model selection variables can be set-valued, thus emphasizing a connection with the so-called set-identified models, which have received considerable attention in recent years. The research will provide a natural frequentist counterpart to the commonly used Bayesian approaches to multi-model forecasts.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.