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

数学科学：统计决策理论、贝叶斯分析、概率和计算研究

基本信息

批准号：
8702620
负责人：
James Berger
金额：
$ 67.04万
依托单位：
Purdue Research Foundation
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
1987
资助国家：
美国
起止时间：
1987-07-01 至 1991-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=8702620&HistoricalAwards=false
关键词：
Mathematical Sciences Investigations Statistical Decision

项目摘要

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.

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贝叶斯计算通过正交，蒙特卡洛，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。