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

该提案探讨了贝叶斯非参数中的四个主题 统计 他们的中心是一个被描述为A的过程 下标n，假设有（n +1）个观测值 （n +1）随机数 可观测的随机量是 假设它们是可交换的，它们之间的联系被假设为 概率为零。给定n个观测值， 第（n +1）个观测值福尔斯落入其中一个开放 由给定的排序观测值创建的区间被假定为 是区间数的倒数。（有（n +1）个） 间隔。） 第一个主题涉及发展一个 此过程用于多变量观测的版本。的 第二个主题涉及将程序的使用扩展到 对未来观测值的后验期望的评估。 第四个主题涉及扩展过程的结果， 贝叶斯数据背景下的混合数据分析 分析. 第三个主题是一个理论的发展， 从Bayesian的观点来看。

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.