Bayesian Empirical Likelihood: Data Analysis Tools with Applications in Econometrics

该研究项目将为非生成性模型开发一套连贯的贝叶斯数据分析工具。生成性统计模型提供了一种现象的完整技术描述。这样的模型足够详细，人们可以从中生成完整的数据集，包括在个人层面和人口层面的观察。本质上，生成性模型提供了进入人造世界的途径。这些模型在自然科学中很流行，在那里有可能对世界进行全面和完整的技术描述。相比之下，许多应用领域使用非生成性模型。这类模型的理论基础是描述一种现象的关键特征，而不指定次要特征。这些模型已经在多个领域证明了它们的价值，包括计量经济学，这是本项目考虑的主要应用领域。该项目将专注于传统上依赖于生成性统计模型的贝叶斯方法。贝叶斯范式为开发数据分析技术提供了丰富的环境，以确定模型中的缺陷并补救数据缺陷的影响。该项目将为非生成性模型开发一整套类似的贝叶斯推断和诊断，并将在计量经济学的实质性经验背景下实施它们。该项目涉及三名调查人员之间的国际和多学科合作，为他们的学生提供直接机会。调查人员经常与STEM领域中代表性较低的群体(包括女性和少数族裔)的学生合作，进行交叉指导，加深学生对统计学和计量经济学的看法，并为他们提供对美国和澳大利亚教育制度的优势和劣势的洞察。本研究项目将利用生成模型开发数据分析技术，并对其进行调整，以用于由一组(广义)矩约束指定的非生成性模型。在此背景下，经验似然实现了一种基于经验导出的满足矩约束的似然函数的似然驱动的推理形式。由于许多现有的数据分析技术都是基于可能性的，该项目将考虑这些模型的经验似然版本。最终目标是通过扩展基于矩的建模器的工具包来改进基于矩的模型数据分析。研究人员将：1)在贝叶斯经验似然背景下开发一套案例影响诊断，并调查这些诊断的理论和经验属性；2)开发贝叶斯经验似然方法进行假设检验、模型比较和模型平均，并注意零假设的表述；以及3)将根据第1点和第2点开发的工具应用于一系列计量经济学应用，例如，资产价格和短期利率的建模。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。

This research project will develop a cohesive set of Bayesian data analysis tools for non-generative models. A generative statistical model provides a complete technical description of a phenomenon. Such a model is detailed enough that one can generate a full data set from it, including observations at the individual level as well as the population level. In essence, the generative model provides access to an artificial world. These models are prevalent in the physical sciences where there is the possibility of having a full and complete technical description of the world. In contrast, many applied fields make use of non-generative models. This type of model is based on theory that describes the key features of a phenomenon while leaving minor features unspecified. These models have proven their worth in a variety of fields, including econometrics, the main area of application considered in this project. The project will focus on Bayesian methods that have traditionally relied on generative statistical models. The Bayesian paradigm provides a rich environment for the development of data-analytic techniques for identification of deficiencies in models and remediation of the effects of shortcomings of the data. The project will develop a full suite of analogous Bayesian inferences and diagnostics for non-generative models and will implement them in substantive empirical contexts from econometrics. The project involves international and multidisciplinary collaboration between the three investigators with direct opportunities for their students. Often working with students from underrepresented groups in STEM fields, including women and minorities, the investigators will engage in cross-mentoring to deepen the students' views of both statistics and econometrics and to provide them with insight into the strengths and weaknesses of the educational systems in the US and Australia.This research project will take techniques developed for data analysis with generative models and adapt them for use with non-generative models specified by a set of (generalized) moment constraints. Within this context, empirical likelihood enables a form of likelihood-driven inference based on an empirically derived likelihood function satisfying the moment constraints. As many existing data analysis techniques are likelihood based, the project will consider empirical likelihood versions of these models. The eventual goal is to improve moment-based model data analysis by expanding the toolkit for the moment-based modeler. The researchers will: 1) Develop a suite of case influence diagnostics within the Bayesian empirical likelihood context and investigate the theoretical and empirical properties of these diagnostics; 2) Develop Bayesian empirical likelihood methods for hypothesis testing, model comparison, and model averaging, with attention to formulation of the null hypothesis; and 3) Apply the tools developed under points 1 and 2 to a range of econometric applications; for example, to the modeling of asset prices and short-term interest rates.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.