Algebraic Statistics / Edition 1

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Overview

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 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.

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Editorial Reviews

Booknews
Considers the application of polynomial algebra to experimental design, discrete probability, and statistics. The book begins with an introduction to Gr<:o>bner bases and a description of their application to experimental design. The authors, who are European professors, then cover the binary case with new application to coherent systems in reliability and two level factorial designs. This paves the way for the application of computer algebra to discrete probability and statistical modeling via the concept of an algebraic statistical model. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

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
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

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