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

这个团队将在四个领域工作：决策理论， 贝叶斯分析、概率和计算。 决定- 要考虑的理论问题包括多变量 估计，制定估计损失的方法， 经典和层次的排序和选择 贝叶斯模型、序贯决策问题和自适应 估计和测试。 贝叶斯分析中的问题， 包括发展稳健的贝叶斯方法 用于检验精确假设，分层贝叶斯分析， 密度和函数估计，以及 没有提供信息的前科 在概率论和序列理论中， 分析，要考虑的问题包括研究分支 扩散，一维吉布斯状态的研究， 生存分析中的序贯方法， 分配理论 最后，计算问题是 考虑包括通过求积、Monte进行贝叶斯计算 卡洛，和近似，随机变量的生成，以及 密度模拟的相关问题。 这个研究小组将研究一系列广泛的问题 在统计学和概率中， 提供更有效和更全面的方法， 产生信息，从数据中提取信息， 做出明智的决定。 克服计算问题是 这是在其中一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.