Algebraic Statistics —— Computational Commutative Algebra in Statistics

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ISBN: 9781584882046 出版年：2000 页码：180 Pistone, Giovanni Riccomagno, Eva Wynn, Henry P CRC Press

INTRODUCTION History and Motivation Overview Computer Algebra Summary ALGEBRAIC MODELS Models Polynomials and Polynomial Ideals Term-Orderings Division Algorithm All Ideals Are Finitely Generated Varieties and Equations Grobner Bases Properties of Grobner Basis Elimination Theory Polynomial Functions and Quotients by Ideals Hilbert Function Further Topics THE DIRECT THEORY Designs and Design Ideals Computing the Grobner basis of a design Operations with Designs Examples Span of a Design Models and Identifiability Quotients Examples The Fan of an Experimental Design Subsets and Sequential Algorithms Regression Analysis Other Topics TWO-LEVEL DESIGNS. APPLICATION IN LOGIC AND RELIABILITY The binary case: Boolean Representations Reliability: Coherent Systems are Minimal Fan Designs Two Level Factorial Design: Contrasts and Orthogonality PROBABILITY AND STATISTICS Random Variables on a Finite Support Moments Probability Algebraic Representation of Exponentials Generating Functions Generating Functions and Exponential Models Examples and Further Applications Statistical Modelling Likelihoods and Sufficient Statistics A Ring of Random Variables Score Function and Information