Mathematical Sciences: Chance Processes and the Foundation of Statistics

先验信念可以用部分可交换性的概念来表征，通过使用deFinetti定理作为范例，根据概率的对称性来描述概率的凸集。以前提出的统计程序也将使用通常的频率主义标准，如一致性和渐近正态性进行检查。将考虑检验对政策分析有用的统计模型的假设，并评价这些模型在这些假设失效情况下的表现。统计学的基础包括先验信念的概念和它们的特征，以及它们与良好统计程序的关系。标准统计程序在非标准条件下的表现如何，以及如何测试条件以验证假设是本项目要考虑的其他基本问题。

Prior beliefs can be characterized using ideas of partial exchangeability by describing certain convex sets of proba- bilities in terms of their symmetry properties using deFinetti's theorem as a paradigm. Statistical procedures suggested by priors will also be examined using usual frequentist criteria like consistency and asymptotic normality. Tests of the assumptions for statistical models useful for policy analysis will be considered and the performance of such models under failure of these assumptions will evaluated. The foundations of statistics include concepts of prior beliefs and their characterization and their relation to good statistical procedures. How standard statistical procedures behave under nonstandard conditions and how to test the conditions to verify assumptions are other basic issues to be considered in this project.