References: |
1. Statistica Sinica: special issue on Algebraic Statistics and Computational Biology, 17:4 (2007). 2. Journal of Symbolic Computation: special issue on Computational Algebraic Statistics, 41:2 (2006). 3. J. Abbott and A. Bigatti and M. Kreutzer and L. Robbiano, Computing ideals of points, Journal of Symbolic Computation, 30:4, 341–356 (2000). 4. E.S. Allman and J.A. Rhodes, Identifying evolutionary trees and substitution parameters for the general Markov model with invariable sites, Mathematical Biosciences, 211:1, 18-33 (2008). 5. S. Aoki and A. Takemura, Markov bases for design of experiments with three-level factors, In Geometric and Algebraic Methods in Statistics (eds. P. Gibilisco, E. Riccomagno, M.P. Rogantin and H.P. Wynn), Cambridge University Press, Cambridge (forthcoming). 6. S. Aoki, A. Takemura and R. Yoshida, Indispensable monomials of toric ideals and Markov bases, Journal of Symbolic Computation, 43, 490–507 (2008). 7. R.A. Bailey, The decomposition of treatment degrees of freedom in quantitative factorial experiments, J. R. Statist. Soc., B 44:1, 63–70 (1982). 8. R.A. Bailey, P.J. Cameron and R. Connelly, Sudoku, Gerechte Designs, Resolutions, Affine Space, Spreads, Reguli, and Hamming Codesread, Ameri- can Math. Monthly (May 2008). 9. T. Becker and V. Weispfenning, The Chinese remainder problem, multivariate interpolation, and Gr¨obner bases, in ISSAC 91: Proceedings of the 1991 international symposium on symbolic and algebraic computation, 64–69 (1991). 10. N. Beerenwinkel, N. Eriksson and B. Sturmfels, Conjunctive Bayesian networks, Bernoulli 13:4, 893-909 (2007). 11. Y. Berstein, J. Lee, H. Maruri-Aguilar, S. Onn, E. Riccomagno, R. Weismantel, H.P. Wynn, Nonlinear Matroid Optimization and Experimental Design, SIAM Journal on Discrete Mathematics 22:3, 901-919 (2008). 12. Y. Berstein, H. Maruri-Aguilar, S. Onn, E. Riccomagno, H.P. Wynn, Minimal average degree aberration and the state polytope for experimental design, MUCM report no. 07/07. 13. J. Besag and P. Clifford, Generalized Monte Carlo significance tests, Biometrika, 76, 633– 642 (1989). 14. Y.M. Bishop, S.E. Fienberg and P.W. Holland, Discrete multivariate analysis: theory and practice, x+557. MIT Press, Cambridge, MA (1977). 15. J. Bochnak, M. Coste and M.F. Roy, Real algebraic geometry, x+430. Springer-Verlag, Berlin (1998). 16. CoCoATeam, CoCoA : a system for doing Computations in Commutative Algebra, Available at http://cocoa.dima.unige.it 17. M. Caboara and E. Riccomagno, An algebraic computational approach to the identifiability of Fourier models, Journal of Symbolic Computation, 26:2, 245–260 (1998). 18. E. Carlini and F. Rapallo, Algebraic modelling of category distinguishability, In Geometric and Algebraic Methods in Statistics (eds. P. Gibilisco, E. Riccomagno, M.P. Rogantin and H.P. Wynn), Cambridge University Press, Cambridge (forthcoming). 19. M. Casanellas and J. Fernndez-Snchez, Performance of a new invariants method on homogeneous and non-homogeneous quartet trees, Molecular Biology and Evolution, 24:1, 288–293 (2007). 20. F. Catanese, S. Ho¸sten, A. Khetan and B. Sturmfels, The maximum likelihood degree, Amer. J. Math. 128:3, 671–697 (2006). 21. Y. Chen, I.H. Dinwoodie and S. Sullivant, Sequential importance sampling for multiway tables, The Annals of Statistics, 34:1, 523-545 (2006). 22. D. Cox, J. Little and D. O’Shea, Ideal, Varieties, and Algorithms, xvi+551. Springer- Verlag, New York (2008), Third Edition. 23. P. Diaconis and N. Eriksson, Markov bases for noncommutative Fourier analysis of ranked data, J. Symbolic Comput. 41:2, 182–195 (2006). 24. P. Diaconis and B. Sturmfels, Algebraic algorithms for sampling from conditional distributions, Annals of Statistics, 26:1, 363–397 (1998). 25. E. Dimitrova, A. Jarrah, R. Laubenbacher, and B. Stigler, A Gr¨obner fan method for biochemical network modeling, ISSAC Proceedings, 122-126 (2007). 26. I.H. Dinwoodie, The Diaconis-Sturmfels algorithm and rules of succession, Bernoulli 4:3, 401–410 (1998). 27. A. Dobra, Markov Bases for decomposable graphical models, Bernoulli, 9, 1093–1108 (2003). 28. M. Drton, Algebraic techniques for Gaussian models, In Prague Stochastics (M. Huskova, M. Janzura Eds.), 81–90 (2006). 29. M. Drton, Likelihood ratio tests and singularities, Annals of Statistics (to appear). 30. M. Drton and S. Sullivant, Algebraic statistical models, Statistica Sinica, 17:4, 1273–1297 (2007). 31. N. Eriksson, S.E. Fienberg, A. Rinaldo and S. Sullivant, Polyhedral conditions for the nonexistence of the MLE for hierarchical log-linear models. J. Symbolic Comput. 41:2, 222–233 (2006). 32. S.E. Fienberg, P. Hersh, A. Rinaldo and Y. Zhou, Maximum likelihood estimation in latent class models For contingency table data, In Geometric and Algebraic Methods in Statistics (eds. P. Gibilisco, E. Riccomagno, M.P. Rogantin and H.P. Wynn), Cambridge University Press, Cambridge (forthcoming). 33. S.E. Fienberg and A. Slavkovic, Preserving the confidentiality of categorical statistical data bases when releasing information for association rules. Data Min. Knowl. Discov. 11:2, 155–180 (2005). 34. R. Fontana, G. Pistone and M.P. Rogantin, Classification of two-level factorial fractions, Journal of Statistical Planning and Inference, 87:1, 149–172 (2000). 35. R. Fontana and M.P. Rogantin, Indicator function and sudoku designs, In Geometric and Algebraic Methods in Statistics (eds. P. Gibilisco, E. Riccomagno, M.P. Rogantin and H.P. Wynn), Cambridge University Press, Cambridge (forthcoming). 36. L.D. Garcia, M. Stillman and B. Sturmfels, Algebraic geometry of Bayesian networks, J. Symbolic Comput. 39:3-4, 331–355 (2005). 37. D. Geiger, C. Meek and B. Sturmfels, On the toric algebra of graphical models, The Annals of Statistics 34:3, 1463–1492 (2006). 38. P. Gibilisco, E. Riccomagno, M.P. Rogantin and H.P. Wynn (eds.), Geometric and algebraic methods in statistics. Cambridge University Press, Cambridge (forthcoming). 39. H. Hara, A. Takemura and R. Yoshida, A Markov basis for conditional test of common diagonal effect in quasi-independence model for two-way contingency tables, arXiv:0802.2603. 40. C. Kang and J. Tian, Polynomial constraints in causal Bayesian networks, In Proceedings of the Conference on Uncertainty in Artificial Intelligence (UAI), 2007. 41. A. Krampe and S. Kuhnt, Bowker’s test for symmetry and modifications within the algebraic framework, Computational Statistics and Data Analysis, 51:9, 4124–4142 (2007). 42. A. Krampe and S. Kuhnt, Model selection for contingency tables with algebraic statistics, In Geometric and Algebraic Methods in Statistics (eds. P. Gibilisco, E. Riccomagno, M.P. Rogantin and H.P. Wynn), Cambridge University Press, Cambridge (forthcoming). 43. M. Kreuzer and L. Robbiano, Computational commutative algebra, 1, x+321. Springer- Verlag, Berlin (2000). 44. M. Kreuzer and L. Robbiano, Computational commutative algebra, 2, x+586. Springer- Verlag, Berlin (2008). 45. Z. Lin, L. Xu and Q. Wu, Applications of Gr¨obner bases to signal and image processing: a survey, Linear Algebra and its Applications, 391, 169–202 (2004). 46. P. Malkin, Computing Markov bases, Gr¨obner bases, and extreme rays, x+223. Ph.D. thesis, Universit´e Catholique de Louvain (2007). 47. H. Maruri-Aguilar, Algebraic statistics in experimental design, Department of Statistics, University of Warwick (2007). 48. H. Maruri-Aguilar, R. Notari and E. Riccomagno, On the description and identifiability analysis of mixture designs, Statistica Sinica 17:4, 1417–1440 (2007). 49. H. Maruri-Aguilar and E. Riccomagno, A model selection algorithm for mixture experiments including process variables, In Proceedings of Moda8 (J Lopez-Fidalgo, J Rodrguez- Daz, B Torsney eds.), 107-114 (2007). 50. H. Maruri-Aguilar and H.P. Wynn, Generalised design: interpolation and statistical modelling over varieties, In Geometric and Algebraic Methods in Statistics (eds. P. Gibilisco, E. Riccomagno, M.P. Rogantin and H.P. Wynn), Cambridge University Press, Cambridge (forthcoming). 51. T. Mora and L. Robbiano, The Gr¨obner fan of an ideal, Journal of Symbolic Computation, 6, 183–208 (1988). 52. S. Onn and B. Sturmfels, Cutting corners, Advances in Applied Mathematics, 23:1, 29–48 (1999). 53. L. Pachter and B. Sturmfels (eds.), Algebraic statistics for computational biology, 420. Cambridge University Press, Cambridge (2005). 54. J. Pearl, Causality. Models, reasoning, and inference, xvi+384. Cambridge University Press, Cambridge (2000). 55. G. Pistone, E. Riccomagno and H. P. Wynn, Algebraic Statistics, xvii+160. Chapman & Hall/CRC, Boca Raton (2001). 56. G. Pistone and M.P. Rogantin, Indicator function and complex coding for mixed fractional factorial designs, Journal of Statistical Planning and Inference, 138:3:1, 787–802 (2008). 57. G. Pistone and H.P. Wynn, Generalised confounding with Gr¨obner bases, Biometrika, 83:3, 653–666 (1996). 58. F. Rapallo, Algebraic Markov bases and MCMC for two-way contingency tables, Scandinavian Journal of Statistics, 30, 385–397 (2003). 59. F. Rapallo, Algebraic exact inference for rater agreement models, Stat. Methods Appl. 14:1, 45–66 (2005). 60. F. Rapallo, Markov bases and structural zeros, J. Symbolic Comput. 41:2, 164–172 (2006). 61. E. Riccomagno and J.Q. Smith, Identifying a cause in models which are not simple Bayesian networks, In Proc. IPMU, 1345–1322 (2004). 62. E. Riccomagno and J.Q. Smith, The geometry of causal probability trees that are algebraically constrained, In Search for Optimality in Design and Statistics: Algebraic and Dynamical System Methods (L Pronzato and A A Zigljavsky eds.), 95-129 (2008). 63. E. Riccomagno and J.Q. Smith, The causal manipulation of chain event graphs, http://arxiv.org/abs/0709.3380. 64. E. Riccomagno and J.Q. Smith, Algebraic causality: Bayes nets and beyond. CRiSM Paper No. 07-3 (2007). 65. H. Scheff´e, Experiments with mixtures, J. Roy. Statist. Soc. Ser. B, 20, 344–360 (1958). 66. H. Scheff´e, The simplex-centroid design for experiments with mixtures, J. Roy. Statist. Soc. Ser. B, 25, 235–263 (1963). 67. G. Shafer, The art of causal conjecture, 552. MIT Press, Cambridge (1996). 68. B. Sturmfels, Solving systems of polynomial equations, CBMS Reg. Conf. Ser. Math., Washington DC (2002). 69. S. Sullivant, Algebraic geometry of Gaussian Bayesian networks, Advances in Applied Mathematics (to appear). 70. K.Q. Ye, Indicator function and its application in two level factorial designs, The Annals of Statistics, 31:3, 984–994 (2003). |