Mathematical Sciences: Chance Processes and the Foundation of Statistics

先验信念可以用部分可交换的思想来刻画，方法是以DeFinetti定理为范例，根据某些凸概率集的对称性来描述它们。还将使用一致性和渐近正态等常见的频率标准来检查先验数据建议的统计程序。将对对政策分析有用的统计模型的假设进行测试，并将评估这些假设失效时这些模型的表现。统计学的基础包括先前信念的概念及其特征及其与良好统计程序的关系。标准统计程序在非标准条件下如何运作，以及如何测试条件以验证假设，这些都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.