Algebraic Statistics
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Algebraic Statistics : Computational Commutative Algebra in Statistics

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Description

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 Grobner bases and a thorough description of their applications to experimental design. A special chapter covers the binary case with new application to coherent systems in reliability and two level factorial designs. The work paves the way, in the last two chapters, for the application of computer algebra to discrete probability and statistical modelling through the important concept of an algebraic statistical model. As the first book on the subject, Algebraic Statistics presents many opportunities for spin-off research and applications and should become a landmark work welcomed by both the statistical community and its relatives in mathematics and computer science.show more

Product details

  • Hardback | 184 pages
  • 166.9 x 231.9 x 28.2mm | 716.68g
  • Taylor & Francis Inc
  • CRC Press Inc
  • Bosa Roca, United States
  • English
  • 20 black & white tables
  • 1584882042
  • 9781584882046
  • 1,247,092

Review quote

..."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, 2001show more

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 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 Informationshow more