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| List of contributors | p. ix |
| Preface | p. xiii |
| Frequently used notations and symbols | p. xvi |
| Algebraic and geometric methods in statistics The editors | p. 1 |
| Contingency tables | p. 25 |
| Maximum likelihood estimation in latent class models for contingency table data | p. 27 |
| Algebraic geometry of 2x2 contingency tables | p. 63 |
| Model selection for contingency tables with alg... MORE | p. 83 |
| Markov chains, quotient ideals and connectivity with positive margins | p. 99 |
| Algebraic modelling of category distinguishability | p. 111 |
| The algebraic complexity of maximum likelihood estimation for bivariate missing data | p. 123 |
| The generalised shuttle algorithm | p. 135 |
| Designed experiments | p. 157 |
| Generalised design: interpolation and statistical modelling over varieties | p. 159 |
| Design of experiments and biochemical network inference | p. 175 |
| Replicated measurements and algebraic statistics | p. 187 |
| Indicator function and sudoku designs | p. 203 |
| Markov basis for design of experiments with three-level factors | p. 225 |
| Information geometry | p. 239 |
| Introduction to non-parametric estimation | p. 241 |
| The Banach manifold of quantum states | p. 257 |
| On quantum information manifolds | p. 265 |
| Axiomatic geometries for text documents | p. 277 |
| Exponential manifold by reproducing kernel Hilbert spaces | p. 291 |
| Geometry of extended exponential models | p. 307 |
| Quantum statistics and measures of quantum information | p. 327 |
| Information geometry and algebraic statistics | p. 339 |
| Algebraic varieties vs. differentiable manifolds in statistical models | p. 341 |
| On-line supplements (available for download from www.cambridge.org/9780521S96191) | p. 367 |
| Coloured figures for Chapter 2 | p. 369 |
| Maximum likelihood estimation in latent class models for contingency table data | p. 373 |
| The generalised shuttle algorithm | p. 395 |
| Indicator function and sudoku designs | p. 408 |
| Replicated measurements and algebraic statistics | p. 424 |
| Geometry of extended exponential models | p. 427 |
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