Mathematical Sciences: Sequential Analysis, Regression, Resampling and New Applications

数学科学：序列分析、回归、重采样和新应用

• 批准号: 8817204
• 负责人: Herman Chernoff
• 金额: $ 6.87万
• 依托单位: Harvard University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-01-01 至 1991-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8817204&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Sequential; Analysis; Regression

The investigator, Herman Chernoff, will continue his work in sequential analysis. One problem is that of deciding the sign of m, the drift of Brownian motion. Assuming the cost of a wrong decision to be independent of m and the sampling cost to be proportional to time multiplied by the square of the drift for bounded sampling time. Chernoff will examine the effect of normal priors and mixtures of normal and point mass priors form. Another problem to be investigated is that of serial dependence in quality control. Chernoff will also examine a robust method for the problem of missing explanatory variables in a regression model. In the area of simulation the Chernoff will study the asymptotic validity of the "bootstrap" method as well as a two- stage approximation of a posterior distribution. It is hoped that these and other statistical methods will prove useful in problems in astronomy. He will also study the possibility of applying data analytic and pattern recognition techniques to the identification of common subsequences in long strings that occur in biological problems.

调查人员赫尔曼·切尔诺夫将继续他的顺序分析工作。一个问题是确定m的符号，即布朗运动的漂移。假设错误决策的成本与m无关，并且采样成本与时间乘以有限采样时间的漂移的平方成比例。切尔诺夫将研究正常先验以及正常质量先验和点质量先验的混合形式的影响。另一个需要研究的问题是质量控制中的串联依赖问题。切尔诺夫还将研究一种稳健的方法来解决回归模型中缺失解释变量的问题。在模拟方面，Chernoff将研究“Bootstrap”方法的渐近有效性以及后验分布的两阶段近似。人们希望这些统计方法和其他统计方法将在天文学问题上被证明是有用的。他还将研究将数据分析和模式识别技术应用于识别生物问题中出现的长串中的公共子序列的可能性。