Mathematical Sciences: Investigations in Statistical Decision Theory, Bayesian Analysis, Probability and Computation

该团队将在四个领域开展工作：决策理论、贝叶斯分析、概率和计算。要考虑的决策理论问题包括多元估计、估计损失方法的发展、经典贝叶斯模型和层次贝叶斯模型的排序和选择、顺序决策问题和自适应估计和测试。本课程将讨论贝叶斯分析中的问题，包括用于检验精确假设的稳健贝叶斯方法的发展、层次贝叶斯分析、密度和函数估计，以及非信息先验的发展。在概率论和序列分析中，要考虑的问题包括分支扩散的研究、一维吉布斯态的研究、生存分析中的序列方法以及分布理论中的某些问题。最后，要考虑的计算问题包括贝叶斯计算，通过正交，蒙特卡罗和近似，随机变量的生成，以及密度模拟的相关问题。该研究小组将研究统计学和概率论中的广泛问题，其解决方案将为产生信息、从数据中提取信息和做出明智决策提供更有效和更全面的方法。克服计算问题是在这些方面取得进展的必要条件。

This team will work in four areas: decision theory, Bayesian analysis, probability, and computation. The decision- theoretic problems to be considered include multivariate estimation, the development of estimated loss methodology, ranking and selection for both classical and hierarchical Bayesian models, sequential decision problems and adaptive estimation and testing. Problems in Bayesian analysis that will be addressed include the development of robust Bayesian methods for testing of precise hypotheses, hierarchical Baysian analysis, density and function estimation, and the development of noninformative priors. Within probability theory and sequential analysis, problems to be considered include study of branching diffusions, investigation of one-dimensional Gibbs states, sequential methods in survival analysis, and certain problems in distribution theory. Finally, the computational problems to be considered include Bayesian calculation via quadrature, Monte Carlo, and approximations, generation of random variables, and related problems of density simulation. This research team will work on a broad spectrum of problems in statistics and probability, the solutions to which will provide more efficient and more comprehensive methods for producing information, extracting information from data and making informed decisions. Overcoming computational problems is a requirement for progress on some of these fronts.