Grobner bases and their applications in statistics and related fields.
by
Sujay Datta
Dept. of Mathematics, Statistics & Computer Sc., Northern Michigan University, Marquette, MI 49855

Algebraic methods have been used extensively in the construction of designs of experiments having certain desirable properties. For example, abstract algebra (group theory) has been used to construct balanced factorial designs with specific aliasing properties, and to deal with the identifiability problem in such designs.

Other uses of polynomial algebra and related algebraic methods can be found in probability, Boolean logic, statistical modeling, Monte Carlo sampling, and Bayes networks. Methods based on Grobner bases have proved themselves to be widely useful in this context. Here we start with the preliminary algebraic groundwork needed for defining Grobner bases. Then we go on to define those bases, discuss some of their properties, and conclude with a few examples of their usefulness in statistics.

Date received: September 11, 2003