그뢰브너 기저와 지시함수와의 관계 = $Gr\ddot{o}bner$ basis versus indicator function

다국어 초록 (Multilingual Abstract)

Many problems of confounding and identifiability for polynomial models in an experimental design can be solved using methods of algebraic geometry. The theory of $Gr\ddot{o}bner$ basis is used to characterize the design. In addition, a fractional factorial design can be uniquely represented by a polynomial indicator function. $Gr\ddot{o}bner$ bases and indicator functions are powerful computational tools to deal with ideals of fractions based on each different theoretical aspects. The problem posed here is to give how to move from one representation to the other. For a given fractional factorial design, the indicator function can be computed from the generating equations in the $Gr\ddot{o}bner$ basis. The theory is tested using some fractional factorial designs aided by a modern computational algebra package CoCoA.

참고문헌 (Reference)

1 Plackett, R. L, "The design of optimum multifactorial experiments" 33 : 305-325, 1946

2 Zhang, R, "Optimal blocking of two-level fractional factorial designs" 91 : 107-121, 2000

3 Ye,K.Q, "Indicator functions and its application in two-level factorial designs" 31 : 984-994, 2003

4 Pistone, G, "Indicator function and complex coding for mixed fractional factorial designs" 138 : 107-121, 2008

5 Cox, D, "Ideal, varieties, and algorithms" Spring-Verlag 1992

6 Pistone, G, "Generalized confounding with Gr¨obner bases" 83 : 653-666, 1996

7 Fontana, R, "Classification of two-level factorial fractions" 87 : 149-172, 2000

8 Pistone, G, "Algebraic statistics method for DOE" Unpublished Manuscript 2006

9 DongKwonPark, "A New Approach for Selecting Fractional Factorial Designs" 한국데이터정보과학회 14 (14): 707-714, 2003