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Algebraic and Geometric Methods in Statistics

ISBN: 9780521896191 | 0521896193
Edition: 1st
Format: Hardcover
Publisher: Cambridge University Press
Pub. Date: 11/30/2009

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SummaryTable of Contents
This up-to-date account of algebraic statistics and information geometry explores the emerging connections between the two disciplines, demonstrating how they can be used in the design of experiments and how they benefit our understanding of statistical models. This new approach to classical statistical problems also raises brand new scientific questions.

An up-to-date account of algebraic statistics and information geometry, which also explores the emerging connections between these two disciplines.
List of contributorsp. ix
Prefacep. xiii
Frequently used notations and symbolsp. xvi
Algebraic and geometric methods in statistics The editorsp. 1
Contingency tablesp. 25
Maximum likelihood estimation in latent class models for contingency table datap. 27
Algebraic geometry of 2x2 contingency tablesp. 63
Model selection for contingency tables with alg... MOREp. 83
Markov chains, quotient ideals and connectivity with positive marginsp. 99
Algebraic modelling of category distinguishabilityp. 111
The algebraic complexity of maximum likelihood estimation for bivariate missing datap. 123
The generalised shuttle algorithmp. 135
Designed experimentsp. 157
Generalised design: interpolation and statistical modelling over varietiesp. 159
Design of experiments and biochemical network inferencep. 175
Replicated measurements and algebraic statisticsp. 187
Indicator function and sudoku designsp. 203
Markov basis for design of experiments with three-level factorsp. 225
Information geometryp. 239
Introduction to non-parametric estimationp. 241
The Banach manifold of quantum statesp. 257
On quantum information manifoldsp. 265
Axiomatic geometries for text documentsp. 277
Exponential manifold by reproducing kernel Hilbert spacesp. 291
Geometry of extended exponential modelsp. 307
Quantum statistics and measures of quantum informationp. 327
Information geometry and algebraic statisticsp. 339
Algebraic varieties vs. differentiable manifolds in statistical modelsp. 341
On-line supplements (available for download from www.cambridge.org/9780521S96191)p. 367
Coloured figures for Chapter 2p. 369
Maximum likelihood estimation in latent class models for contingency table datap. 373
The generalised shuttle algorithmp. 395
Indicator function and sudoku designsp. 408
Replicated measurements and algebraic statisticsp. 424
Geometry of extended exponential modelsp. 427
Table of Contents provided by Ingram. All Rights Reserved.


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