ぱらぱらめくる『Algebraic and Geometirc Methods in Statistics』目次

Algebraic and Geometric Methods in Statistics

作者: Paolo Gibilisco,Eva Riccomagno,Maria Piera Rogantin,Henry P. Wynn
出版社/メーカー: Cambridge University Press
発売日: 2009/10/22
メディア: ハードカバー
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第３章は先行してこちら
目次
- 1. Algebraic and geometric methods in statistics
- Part I. Contingency Tables:
  - 2...8 は分割表とその周辺度数制約や、観察分割表とモデルとの整合性に関すること
  - 9... は分割表を対称性、割り付け方などの観点から見て、「スタディデザイン論」としての統計学との関連すること
  - 2. Maximum likelihood estimation in latent class model
  - 3. Algebraic geometry of 2 x 2 contingency tables
  - 4. Model selection for contingency tables with algebraic statistics
  - 5. Markov chains, quotient ideals, and connectivity
  - 6. Algebraic category distinguishability
  - 7. Algebraic complexity of MLE for bivariate missing data
  - 8. The generalized shuttle algorithm
  - 9. Generalised design
  - 10. Design of experiments and biochemical network inference
  - 11. Replicated measurements and algebraic statistics
  - 12. Indicator function and sudoku designs
  - 13. Markov basis for design of experiments and three-level factors
- Part III. Information Geometry:
  - 確率分布(がパラメタ表示されていることを使って)を点に対応させると、確率分布たちが多様体をなす、そんな話
  - 14. Non-parametric estimation
  - 15. Banach manifold of quantum states
  - 16. On quantum information manifolds
  - 17. Axiomatic geometries for text documents
  - 18. Exponential manifold by reproducing kernel Hilbert spaces
  - 19. Extended exponential models
  - 20. Quantum statistics and measures of quantum information
- Part IV. Information Geometry and Algebraic Statistics:
  - 21. Algebraic varieties vs differentiable manifolds
- Part V. On-Line Supplements
  - 22. Maximum likelihood estimation in latent class models
  - 23. The generalized shuttle algorithm
  - 24. Indicator function and sudoku designs
  - 25. Replicated measurements and algebraic statistics
  - 26. Extended exponential models