Mathematical Sciences: Bayesian Statistical Theory and Methodology

贝叶斯统计理论和 方法福尔斯分为五类：（1）发展 用于分析的适当统计模型和方法 选择的数据和其他类型的非随机样本通常 遇到的。 特别强调的是， 选择样本中的信息与不受限制的 随机抽样 (2)结合专家意见的问题， 包括一项正式的研究， 可能与他们的真实意见不同， 判断给定的组合规则是否 一个可接受的。 (3)最佳检查和 控制，其中有必要安排一系列昂贵的 检查一个随机过程，以便尽快检测 尽可能避免过程失控，或 已经进入了某个理想的目标区域 (4)最优问题 决策者团队的每个成员 仅接收有关a中的观测的部分信息， 连续样本，他们不能直接与每个 其他，他们必须制定一个最佳战略， 停止这个过程。 (5)发展适当的 贝叶斯统计方法用于各种法律的设置。 这项研究是在贝叶斯统计的一般领域， 一种统计决策方法， 在收集新信息之前存在的相关知识 与问题有关的数据。 这背后的一般理论 这种方法并不新鲜，但实际上对 约会 这是因为数学方程需要 解决了即使使用一点点先验信息也需要 大量的计算能力和聪明的算法， 而且，直到最近，这种计算资源还没有被 一般可用。 随着所需资源越来越多， 这项研究的潜在影响越来越大。 作为开创性的贝叶斯方法， 正如这里所提出的，这种方法预计将 传播并彻底改变数据的使用方式， 决策

The proposed research on Bayesian statistical theory and methods falls into five categories: (1) The development of appropriate statistical models and methodology for the analysis of selected data and other types of non-random samples often encountered. Particular emphasis will be placed on comparing the information in a selection sample with that in an unrestricted random sample. (2) Problems of combining expert opinions, including a formal study of how the opinions that experts report might differ from their true opinions, and the development of conditions for determing whether a given rule of combination is an admissible one. (3) Problems of optimal inspection and control in which it is necessary to schedule a sequence of costly inspections of a stochastic process in order to detect as quickly as possible the event that the process has gone out of control or has entered some desirable target area. (4) Problems of optimal stopping in which each member of a team of decision makers receives only partial information about the observations in a sequential sample, they connot communicate directly with each other, and they must develop an optimal strategy for jointly stopping the process. (5) The development of appropriate Bayesian statistical methods for use in various legal settings. This research is in the general area of Bayesian statistics, an approach to statistical decision making that incorporates the pertinent knowledge that exists prior to the collection of new data bearing on the issue. The general theory behind this approach is not new, but has been of little practical use to date. This is because the mathematical equations that need to be solved to use even a little bit of prior information require large amounts of computational horsepower and clever algorithms, and, until recently, such computational resources have not been generally available. With the required resources becoming more commonly available, the potential impact of this research grows. As pathbreaking Bayesian methods for specific practical examples are developed, as is proposed here, this approach is expected to spread and to revolutionize the way data is used to make decisions.