Algebraic Methods in the Design of Experiments
Satoshi Aoki · 2019
Applications of Gröbner basis theory to various problems of statistics arises in early 1990s. One of the first works in this field, a computational algebraic statistics, is given by Pistone and Wynn \citePistone-Wynn-1996, where the Gröbner basis theory is applied to the identifiability problem in the design of experiments. After this work, various algebraic approaches to the problems in the design of experiments are presented by researchers both in the fields of algebra and statistics. In this tutorial, we overview some of early results with a fundamental theory of statistics relating to this field.