http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
computational commutative algebra in statistics
1 online resource (xvii, 160 pages) : illustrations.
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; Gröbner Bases; Properties of Gröbner Basis; Elimination Theory; Polynomial Functions and Quotients by Ideals; Hilbert Function; Further Topics; THE DIRECT THEORY; Designs and Design Ideals; Computing the Gröbner 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.
Giovanni Pistone, Eva Riccomagno, Henry P. Wynn.
Includes bibliographical references (pages 155-157) and index.
Boca Raton, Fla. : Chapman & Hall/CRC, ©2001
Monographs on statistics and applied probability (Series) ; 89