A SURVEY ON COMPUTATIONAL ALGEBRAIC STATISTICS AND ITS APPLICATIONS

Abstract

Computational Algebraic Statistics is a new mathematics-based scien

tific discipline that is combined of three disciplines of Computing, Algebra

and Statistics. This review introduces integrating powerful techniques of

- among other things- Polynomial Algebra, Algebraic Geometry, Group

Theory and Computational Statistics in this new field of Computational

Algebraic Statistics (in brief CAS). CAS currently plays an essential and

powerful role in some importantly applicable fields growing very fast

in recent years, from science to engineering, such as: statistical quality

control, process engineering, computational biology, complex biological

networks, life sciences, data analytics and finance studies.

Furthermore, by combining the theory of algebraic geometry with

graph theory, we point out connections between integer linear program

ming (ILP), mathematical modeling in traffic engineering, logistics man

agement and transportation science.

These methods and algorithms are based on elegant ideas from some

active fields of mathematics and statistics, and their useful applications 

can be potentially found in various scientific and technological sectors