Geodesic
Local and global probabilistic-logic inference in algebraic bayesian networks: a matrix-vector description and issues of sensitivity
Nečetkie sistemy i mâgkie vyčisleniâ, Tome 12 (2017) no. 2, pp. 133-150

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Algorithms and equations for the probabilistic-logic inference of algebraic Bayesian networks are presented in the paper. All types of global consistency are considered and a matrix-vector formalization of consistency conditions is proposed. The paper summarizes results in local posterior inference for different kinds of knowledge patterns. Moreover in this paper we conduct a sensitivity analysis of first problem of a posterior inference for the knowledge pattern built over the ideal of disjuncts and formulate a linear programming problem to find the described estimates.
Keywords: probabilistic graphical models, algebraic Bayesian networks, probabilistic-logic inference, sensitivity analysis, consistency check. 
@article{FSSC_2017_12_2_a4,
     author = {A. A. Zolotin and E. A. Malchevskaia and N. A. Kharitonov and A. L. Tulupyev},
     title = {Local and global probabilistic-logic inference in algebraic bayesian networks: a matrix-vector description and issues of sensitivity},
     journal = {Ne\v{c}etkie sistemy i m\^agkie vy\v{c}isleni\^a},
     pages = {133--150},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FSSC_2017_12_2_a4/}
}
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A. A. Zolotin; E. A. Malchevskaia; N. A. Kharitonov; A. L. Tulupyev. Local and global probabilistic-logic inference in algebraic bayesian networks: a matrix-vector description and issues of sensitivity. Nečetkie sistemy i mâgkie vyčisleniâ, Tome 12 (2017) no. 2, pp. 133-150. http://geodesic.mathdoc.fr/item/FSSC_2017_12_2_a4/