ABSTRACT

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.

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