統計学輪講のスケジュールに戻る．
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.
統計学輪講のスケジュールに戻る．
Tokyo University