A SURVEY ON COMPUTATIONAL ALGEBRAIC STATISTICS AND ITS APPLICATIONS

Abstract

Computational Algebraic Statistics is a new mathematics-based scientific 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 programming (ILP), mathematical modeling in traffic engineering, logistics management 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.