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. Hosten, S. Sullivant, A. Dobra, H. Maruri-Aguilar, R. Laubenbacher, B. Stigler, R. Notari, R. Fontana, S. Aoki, A. Takemura, R. F. Streater, A. Jencová, G. Lebanon, K. Fukumizu, D. Imparato, B. Trivellato, F. Hansen, G. Pistone
Inhaltsangabe
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. Höten 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. Jen¿ová; 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.
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. Höten 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. Jen¿ová; 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.
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