EAPSI: Addressing an Open Problem in Algebraic Statistics

EAPSI：解决代数统计中的一个开放问题

• 批准号: 1515487
• 负责人: Dane Wilburne
• 金额: $ 0.51万
• 依托单位: Wilburne Dane R
• 依托单位国家: 美国
• 项目类别: Fellowship Award
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-06-01 至 2016-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1515487&HistoricalAwards=false
• 关键词: EAPSI; Addressing; Open; Problem; Algebraic

Algebraic statistics is the branch of mathematics concerned with applying techniques and tools from algebra to problems in statistics. This project will be concerned with addressing an open problem in the field of algebraic statistics. The project will be conducted in collaboration with host Prof. Satoshi Kuriki, a renowned statistician, and Prof. Hisayuki Hara, an expert in the field of algebraic statistics, at The Institute of Statistical Mathematics in Tokyo, Japan. The goal of the project is to provide another tool for testing model/data fit for researchers and statisticians to use in applications.The problem to be addressed is the question of how to compute Markov bases for the multi-nomial logistic regression model. Multinomial logistic regression is used to model a categorical dependent variable that can take values in more than two categories in terms of a set of real- or categorically-valued independent variables. A Markov basis is an algebraic object associated to a statistical model that allows one to perform otherwise intractable statistical procedures, such as goodness-of-fit testing and parameter estimation. The goal of the project is to compute a Markov basis for the multinomial logistic regression model and to study its computational complexity. This NSF EAPSI award is funded in collaboration with the Japan Society for the Promotion of Science.

代数统计学是数学的一个分支，主要研究将代数中的技术和工具应用于统计问题。这个项目将关注于解决代数统计领域的一个公开问题。该项目将与日本东京统计数学研究所的著名统计学家Satoshi Kuriki教授和代数统计领域的专家Hisayuki Hara教授合作进行。该项目的目标是为研究人员和统计人员提供另一种用于测试模型/数据拟合的工具，以用于应用。要解决的问题是如何计算多项逻辑回归模型的马尔可夫基的问题。多项逻辑回归用于对分类因变量进行建模，该因变量可以根据一组真实的或分类值自变量在两个以上类别中取值。马尔可夫基是与统计模型相关联的代数对象，允许执行否则难以处理的统计过程，例如拟合优度测试和参数估计。该项目的目标是计算多项逻辑回归模型的马尔可夫基，并研究其计算复杂性。这个NSF EAPSI奖是与日本科学促进协会合作资助的。