日時 2003年 5月27日(火) 15時〜16時40分 場所 経済学部新棟3階第3教室 講演者 Prof. Stephen E. Fienberg(Carnegie Mellon University) 演題 Log-linear Models and Computational Algebra: Old Wine in New Bottles? 概要 This talk combines an overview of some problems in disclosure limitation for multidimensional tables of counts (contingency tables) with their relationship to the statistical theory of log-linear models and a description of their representation in algebraic geometry. Much of the statistical theory of log-linear and logit models for contingency table analysis was set in the 1960s and early 1970s, although subsequent developments in the theory of graphical models were integrated with this earlier work. But then most statisticians thought that the theory was essentially complete, much like the form of a vintage statistical wine. Over essentially the same period of time the mathematical theory of Gr\"{o}bner bases associated with polynomial ideals in algebraic geometry and computational algebra has undergone a similar development. This theory became linked with statistical work in two separate sets of collaborations over the past decade, in particular providing new mathematical bottles for the vintage statistical methods and theory of log-linear models. We explain how the interplay between these two seemingly different mathematical representations has recently generated new results in both areas, opening the possibility of new vintages in new forms of bottles. The practical statistical problems arising in disclosure limitation have provided ongoing motivation to these developments as well as an outlet for application.
Tokyo University