Equations defining probability tree models

Journal of Symbolic Computation - Tập 99 - Trang 127-146 - 2020
Eliana Duarte1, Christiane Görgen2
1Otto-von-Guericke Universität Magdeburg, Germany
2Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany

Tài liệu tham khảo

Allman, 2008, Phylogenetic ideals and varieties for the general Markov model, Adv. Appl. Math., 40, 127, 10.1016/j.aam.2006.10.002 Altham, 1969, Exact Bayesian analysis of a 2×2 contingency table, and Fisher's “exact” significance test, J. R. Stat. Soc. Ser. B, 31, 261 Altham, 1970, The measurement of association in a contingency table: three extensions of the cross-ratios and metrics methods, J. R. Stat. Soc. Ser. B, 31, 395 Altham, 1970, The measurement of association of rows and columns for an r×s contingency table, J. R. Stat. Soc. Ser. B, 32, 63 Barclay, 2015, The dynamic chain event graph, Electron. J. Stat., 9, 2130, 10.1214/15-EJS1068 Barclay, 2013, Refining a Bayesian Network using a Chain Event Graph, Int. J. Approx. Reason., 54, 1300, 10.1016/j.ijar.2013.05.006 Boutilier, 1996, Context-specific independence in Bayesian networks, 115 Casanellas, 2008, Geometry of the Kimura 3-parameter model, Adv. Appl. Math., 41, 265, 10.1016/j.aam.2007.09.003 Collazo, 2018, Chain Event Graphs Collazo, 2015, A new family of non-local priors for chain event graph model selection, Bayesian Anal., 11, 1165, 10.1214/15-BA981 Cox, 2007 Cox, 2011, Toric Varieties, vol. 124 Drton, 2009, Lectures on Algebraic Statistics, vol. 39 Freeman, 2011, Dynamic staged trees for discrete multivariate time series: forecasting, model selection and causal analysis, Bayesian Anal., 6, 279, 10.1214/11-BA610 Garcia Puente, L.D., Petrovic, S., Stillman, M., Sullivant, S., 2005a. GraphicalModels: A package for discrete and Gaussian graphical models. Version 1.0. Garcia Puente, 2005, Algebraic geometry of Bayesian networks, J. Symb. Comput., 39, 331, 10.1016/j.jsc.2004.11.007 Garthwaite, 2005, Statistical method for eliciting probability distributions, J. Am. Stat. Assoc., 100, 680, 10.1198/016214505000000105 Geiger, 2001, Stratified exponential families: graphical models and model selection, Ann. Stat., 29, 505, 10.1214/aos/1009210550 Geiger, 2006, On the toric algebra of graphical models, Ann. Stat., 34, 1463, 10.1214/009053606000000263 Görgen, 2017 Görgen, 2018, Discovery of statistical equivalence classes using computer algebra, Int. J. Approx. Reason., 95, 167, 10.1016/j.ijar.2018.01.003 Görgen, 2018, Equivalence classes of staged trees, Bernoulli, 24, 2676, 10.3150/17-BEJ940 Grayson Lauritzen, 1996, Graphical Models, vol. 17 Miller, 2004 Pistone, 2001, Algebraic Statistics: Computational Commutative Algebra in Statistics, vol. 89 Shafer, 1996 Smith, 2008, Conditional independence and chain event graphs, Artif. Intell., 172, 42, 10.1016/j.artint.2007.05.004 Sullivant, 2018, Algebraic Statistics, 10.1090/gsm/194