Written by pioneers in this exciting new field, Algebraic Statistics introduces the application
of polynomial algebra to experimental design, discrete probability, and statistics. It begins …

Factorial designs are widely used in many scientific and industrial investigations. The
objective of this book is to provide a rigorous, systematic, and up-to-date treatment of the …

The problem of finding a fraction of a two-level factorial design with specific properties is
usually solved within special classes, such as regular or Plackett–Burman designs. We …

Computational algebraic geometry can be used to solve estimability/identifiability problems
in the design of experiments. The key is to replace the design as a set of points by the …

Computer algebra and in particular Gröbner bases are powerful tools in experimental
design (Pistone and Wynn, 1996, Biometrika83, 653–666). This paper applies this algebraic …

The Gröbner basis method in experimental design (Pistone & Wynn, 1996) is developed in a
practical setting. The computational algebraic techniques (Gröbner bases in particular) are …

For a particular experimental design, there is interest in finding which polynomial models
can be identified in the usual regression set up. The algebraic methods based on Gröbner …

Gröbner bases, elimination theory and factorization may be used to perform calculations in
elementary discrete probability and more complex areas such as Bayesian networks …

This work extends the research program of the authors into the design and analysis of
complex experiments. It shows how the special algebraic structures studied in the …

In a mixture experiment the collinearity problems, implied by the sum to one functional
relationship among the factors, have strong consequences on the identification and analysis …