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Algebraic and Geometric Methods in Statistics

$154.99

P. Gibilisco, E. Riccomagno, M. P. Rogantin, H. P. Wynn, S. E. Fienberg, P. Hersh, A. Rinaldo, Y. Zhou, A. Slavkovic, A. Krampe, S. Kuhnt, Y. Chen, I. Dinwoodie, R. Yoshida, E. Carlini, F. Rapallo, S. Hoşten, S. Sullivant, A. Dobra, H. Maruri-Aguilar, R. Laubenbacher, B. Stigler, R. Notari, R. Fontana, S. Aoki, A. Takemura, R. F. Streater, A. Jenčová, G. Lebanon, K. Fukumizu, D. Imparato, B. Trivellato, F. Hansen, G. Pistone
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  • Date Published: November 2009
  • availability: In stock
  • format: Hardback
  • isbn: 9780521896191

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  • 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 design of experiments and how they benefit our understanding of statistical models, in particular, exponential models. This book presents a new way of approaching classical statistical problems and raises scientific questions that would never have been considered without the interaction of these two disciplines. Beginning with a brief introduction to each area, using simple illustrative examples, the book then proceeds with a collection of reviews and some new results written by leading researchers in their respective fields. Part III dwells in both classical and quantum information geometry, containing surveys of key results and new material. Finally, Part IV provides examples of the interplay between algebraic statistics and information geometry. Computer code and proofs are also available online, where key examples are developed in further detail.

    • Chapters written by leading researchers in the field
    • Includes introductory and review chapters, and a glossary of terms from algebraic geometry
    • Online material develops in detail some key examples, and provides computer code, technical material and detailed proofs
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    Product details

    • Date Published: November 2009
    • format: Hardback
    • isbn: 9780521896191
    • length: 382 pages
    • dimensions: 254 x 181 x 23 mm
    • weight: 0.83kg
    • contains: 30 b/w illus. 35 tables
    • availability: In stock
  • Table of Contents

    List of contributors
    Frequently used notations and symbols
    Preface
    1. Algebraic and geometric methods in statistics P. Gibilisco, E. Riccomagno, M. P. Rogantin and H. P. Wynn
    Part I. Contingency Tables:
    2. Maximum likelihood estimation in latent class models S. E. Fienberg, P. Hersh, A. Rinaldo and Y. Zhou
    3. Algebraic geometry of 2 x 2 contingency tables A. Slavkovic and S. E. Fienberg
    4. Model selection for contingency tables with algebraic statistics A. Krampe and S. Kuhnt
    5. Markov chains, quotient ideals, and connectivity Y. Chen, I. Dinwoodie and R. Yoshida
    6. Algebraic category distinguishability E. Carlini and F. Rapallo
    7. Algebraic complexity of MLE for bivariate missing data S. Hoşten and S. Sullivant
    8. The generalized shuttle algorithm A. Dobra and S. E. Fienberg
    Part II. Designed Experiments:
    9. Generalised design H. Maruri-Aguilar and H. P. Wynn
    10. Design of experiments and biochemical network inference R. Laubenbacher and B. Stigler
    11. Replicated measurements and algebraic statistics R. Notari and E. Riccomagno
    12. Indicator function and sudoku designs R. Fontana and M. P. Rogantin
    13. Markov basis for design of experiments and three-level factors S. Aoki and A. Takemura
    Part III. Information Geometry:
    14. Non-parametric estimation R. F. Streater
    15. Banach manifold of quantum states R. F. Streater
    16. On quantum information manifolds A. Jenčová
    17. Axiomatic geometries for text documents G. Lebanon
    18. Exponential manifold by reproducing kernel Hilbert spaces K. Fukumizu
    19. Extended exponential models D. Imparato and B. Trivellato
    20. Quantum statistics and measures of quantum information F. Hansen
    Part IV. Information Geometry and Algebraic Statistics:
    21. Algebraic varieties vs differentiable manifolds G. Pistone
    Part V. On-Line Supplements: Coloured Figures for Chapter 2
    22. Maximum likelihood estimation in latent class models Y. Zhou
    23. The generalized shuttle algorithm A. Dobra and S. E. Fienberg
    24. Indicator function and sudoku designs R. Fontana and M. P. Rogantin
    25. Replicated measurements and algebraic statistics R. Notari and E. Riccomagno
    26. Extended exponential models D. Imparato and B. Trivellato.

  • Resources for

    Algebraic and Geometric Methods in Statistics

    General Resources

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  • Editors

    Paolo Gibilisco, Università degli Studi di Roma 'Tor Vergata'
    Professor Paolo Gibilisco is a Researcher in Mathematical Analysis in the School of Economics at the University of Rome 'Tor Vergata'.

    Eva Riccomagno, Università degli Studi di Genova
    Eva Riccomagno is Associate Professor in the Department of Mathematics at the University of Genova.

    Maria Piera Rogantin, Università degli Studi di Genova
    Maria Piera Rogantin is Associate Professor in the Department of Mathematics at the University of Genova.

    Henry P. Wynn, London School of Economics and Political Science
    Henry P. Wynn is Professor of Statistics at the London School of Economics from 2003, where he leads the Decision Support and Risk Group. He holds the Guy Medal in Silver from the Royal Statistical Society, is an Honorary Fellow of the Institute of Actuaries, and a Fellow of the Institute of Mathematical Statistics.

    Contributors

    P. Gibilisco, E. Riccomagno, M. P. Rogantin, H. P. Wynn, S. E. Fienberg, P. Hersh, A. Rinaldo, Y. Zhou, A. Slavkovic, A. Krampe, S. Kuhnt, Y. Chen, I. Dinwoodie, R. Yoshida, E. Carlini, F. Rapallo, S. Hoşten, S. Sullivant, A. Dobra, H. Maruri-Aguilar, R. Laubenbacher, B. Stigler, R. Notari, R. Fontana, S. Aoki, A. Takemura, R. F. Streater, A. Jenčová, G. Lebanon, K. Fukumizu, D. Imparato, B. Trivellato, F. Hansen, G. Pistone

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