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Algebraic Statistics

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Table of Contents

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 Groebner Bases Properties of Groebner Basis Elimination Theory Polynomial Functions and Quotients by Ideals Hilbert Function Further Topics THE DIRECT THEORY Designs and Design Ideals Computing the Groebner 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


..."authors have been the predominant contributors to the field.... for anyone who wants to learn about, and perhaps contribute to, the field, this monograph is undoubtedly the place to start." -Biometrics, Vol. 57, No. 3, September 2001 "This very challenging monograph demonstrates how Grvbner bases may be used to represent experimental design, probability models and statistical models The book points clearly to the future potential use of algebraic tools." Short Book Reviews, Vol. 21, No. 2, August, 2001

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