The binomial ideal of the intersection axiom for conditional probabilities
Alex Fink
DOI: 10.1007/s10801-010-0253-5
Abstract
The binomial ideal associated with the intersection axiom of conditional probability is shown to be radical and is expressed as an intersection of toric prime ideals. This solves a problem in algebraic statistics posed by Cartwright and Engström.
Pages: 455–463
Keywords: keywords conditional independence; intersection axiom
Full Text: PDF
References
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3. Grayson, D.R., Stillman, M.: Macaulay2, a software system for research in algebraic geometry. Available at
4. Greuel, G.-M., Pfister, G., Schönemann, H.: SINGULAR 3.0-a computer algebra system for polynomial computations. In: Kerber, M., Kohlhase, M. (eds.) Symbolic Computation and Automated Reasoning, The Calculemus-2000 Symposium, pp. 227-233 (2001)
5. Greuel, G.-M., Pfister, G.: primdec.lib, a SINGULAR 3.0 library for computing the primary de- composition and radical of ideals (2005)
6. Herzog, J., Hibi, T., Hreinsdóttir, F., Kahle, T., Rauh, J.: Binomial edge ideals and conditional independence statements. arXiv:
7. Kahle, T.: Binomials.m2, code for binomial primary decomposition in Macaulay2.
8. Sturmfels, B.: Gröbner bases of toric varieties. T\?ohoku Math. J. 43, 249-261 (1991)
9. Stanley, R.P.: Enumerative Combinatorics, vol.
2. Cambridge Studies in Advanced Mathematics, vol.
62. Cambridge University Press, Cambridge (1997)
10. Studený, M.: Probabilistic Conditional Independence Structures, Information Science and Statistics.
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