Mathematical Sciences: Chance Processes

弗里德曼将致力于研究有关统计学基础的问题：如何表征先前的信念，以及这种信念何时会导致良好的统计程序；如何看待高维数据；标准统计程序在非标准条件下会发生什么；如何测试统计模型。这些问题包括：部分互换性和充分性；贝叶斯估计的一致性；后验分布的渐近正态；估计标准误差的Bootstrap技术；回归模型在社会科学数据中的应用。

Freedman will work on questions about the foundations of statistics: how to characterize prior beliefs, and when do such beliefs lead to good statistical procedures; how to look at high dimensional data; what happens to standard statistical procedures under nonstandard conditions; how to test statistical models. These questions include the following topics: partial exchangeability and sufficiency; the consistency of Bayes estimates; asymptotic normality of posterior distributions; the bootstrap technique for estimating standard errors; the application of regression models to social science data.