Mathematical Sciences: Chance Processes and the Foundation of Statistics

先验信念可以用局部的概念来描述， 通过描述概率的某些凸集， 使用deFinetti的对称性， 定理是一种范式。 建议的统计程序 先验也将使用通常的频率标准进行检查 比如一致性和渐近正态性 的测试 对政策分析有用的统计模型假设 将被考虑，这些模型的性能在 这些假设的失败将被评估。 统计学的基础包括先验概念 信仰及其特征及其与善的关系 统计程序。 标准统计程序 在非标准条件下的行为以及如何测试 验证假设的条件是其他基本问题 在这个项目中考虑。

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.