統計学輪講(第10回)

 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.



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Tokyo University