Mathematical Sciences: Foundations and Applications of Bayesian Inference and Decision Theory

本提案检视贝叶斯非参数统计的四个主题。它们的中心是一个描述为a下标n的过程，该过程假设有（n+1）个随机量的（n+1）个观测值。假设观察到的随机量是可交换的，并且假设它们之间的联系的概率为零。给定n个观测值，假设（n+1）个观测值落在由排序给定观测值创建的开放区间中的一个的概率是区间数量的倒数。（有（n+1）个间隔。）第一个主题涉及开发用于多变量观测的该程序的一个版本。第二个主题涉及将该程序的使用扩展到对未来观察的后验期望的评估。第四个主题涉及将该过程的结果扩展到贝叶斯数据分析背景下的混合数据分析。第三个主题是从贝叶斯观点出发的随机化理论的发展。

The proposal examines four topics in Bayesian nonparametric statistics. They center about a procedure described as A subscript n which assumes that there are (n+1) observed values of (n+1) random quantities. The observable random quantities are assumed to be exchangeable and ties among them are assumed to have probability zero. Given n of the observations the probability that the (n+1)st observation falls in one of the open intervals created by the ranked given observations is assumed to be the inverse of the number of intervals. (There are (n+1) intervals.) The first topic involves the development of a version of this procedure for multivariate observations. The second topic involves extending the use of the procedure to the evaluation of the posterior expectation of future observations. The fourth topic involves extending results for the procedure to the analysis of mixture data in the context of Bayesian data analysis. The third topic is the development of a theory of randomization from a Bayesian viewpoint.