EAPSI: Addressing an Open Problem in Algebraic Statistics

Wilburne Dane R, Chicago IL

Investigators

Abstract

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.