G. PISTONE

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Let $(X, Cal X, mu)$ be a measure space, and let $Cal M(X,Cal X,mu)$ denote the set of the $mu$-almost surely strictly positive probability densities. It was shown by G. Pistone and C. Sempi (1995) that the global geometry on $Cal M(X,Cal X,mu)$ can be realized by an affine atlas whose charts are defined locally by the mappings $Cal M(X,Cal...

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The problem of finding a fraction of a two-level factorial design with specic properties is usually solved within special classes, such as regular or Plackett–Burman designs. We show that each fraction of a two-level factorial design is characterized by the ANOVA representation of its polynomial indicator function. In particular, such a...

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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 with an introduction to Gröbner bases and a thorough description of their application to experimental design. A special chapter covers the binary case with...

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 polynomials whose solutions are the design points. The theory and application of Gröbner bases allows one to find a unique saturated model for each so-called...