Algebraic and geometric methods in statistics / edited by Paolo Gibilisco [and others].
- Additional Titles:
- Algebraic & Geometric Methods in Statistics
- Cambridge : Cambridge University Press, 2009.
- Physical Description:
- 1 online resource (xvi, 365 pages) : digital, PDF file(s).
- Additional Creators:
- Gibilisco, Paolo
- Algebraic and geometric methods in statistics -- Contingency tables -- Maximum likelihood estimation in latent class models for contingency table data / S.E. Fienberg [and others] -- Algebraic geometry of 2x2 contingency tables / A.B. Slavković and S.E. Fienberg -- Model selection for contingency tables with algebraic statistics / A. Krampe and S. Kuhnt -- Markov chains, quotient ideals and connectivity with positive margins / Y. Chen, I. Dinwoodie and R. Yoshida -- Algebraic modelling of category distinguishability / E. Carlini and F. Rapallo -- The algebraic complexity of maximum likelihood estimation for bivariate missing data / S. Hosten and S. Sullivant -- The generalised shuttle algorithm / A. Dobra and S.E. Fienberg -- Designed experiments -- Generalised design: interpolation and statistical modelling over varieties / H. Maruri-Aguilar and H.P. Wynn -- Design of experiments and biochemical network inference / R. Laubennacher and B. Stigler -- Replicated measurements and algebraic statistics / R. Notari and E. Riccomagno -- Indicator function and sudoku designs / R. Fontana and M.P. Rogantin -- Markov basis for design of experiments with three-level factors / S. Aoki and A. Takemura -- Information geometry -- Introduction to non-parametric estimation / R.F. Streater -- The Banach manifold of quantum states / R.F. Streater -- On quantum information manifolds / A. Jencova -- Axiomatic geometrics for text documents / G. Lebanon -- Exponenetial manifold by reproducing kernel Hilbert spaces / K. Fukumizu -- Geometry of extended exponential models / D. Imparato and B. Trivellato -- Quantum statistics and measures of quantum information / F. Hansen -- Information geometry and algebraic statistics -- Algebraic varieties vs. differentiable manifolds in statistical models / G. Pistone.
- 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.
- 9780511642401 (ebook)
- Title from publisher's bibliographic system (viewed on 05 Oct 2015).
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