Algebraic Statistics / Edition 1

Algebraic Statistics / Edition 1

by Giovanni Pistone, Eva Riccomagno, Henry P. Wynn
     
 

ISBN-10: 1584882042

ISBN-13: 9781584882046

Pub. Date: 09/05/2000

Publisher: Taylor & Francis

Written by three acknowledged experts in a new and rapidly expanding a rea, Algebraic Statistics explores the application of symbolic computa tion and Grobner Bases to experimental design, discrete probability, a nd statistics. This field is an outgrowth of algebraic geometry with l inks to a variety of other disciplines, including reliability and info rmation

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Overview

Written by three acknowledged experts in a new and rapidly expanding a rea, Algebraic Statistics explores the application of symbolic computa tion and Grobner Bases to experimental design, discrete probability, a nd statistics. This field is an outgrowth of algebraic geometry with l inks to a variety of other disciplines, including reliability and info rmation theory. With no other book available on the subject, this mono graph-style introduction promises to become a landmark work likely to be referenced by both the statistical community and its "relatives" in algebra and computer science.

Product Details

ISBN-13:
9781584882046
Publisher:
Taylor & Francis
Publication date:
09/05/2000
Series:
Chapman & Hall/CRC Monographs on Statistics & Applied Probability Series, #89
Pages:
184
Product dimensions:
6.14(w) x 9.21(h) x 0.50(d)

Related Subjects

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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