# zbMATH — the first resource for mathematics

Solution of the marginal problem and decomposable distributions. (English) Zbl 0752.60009
It is shown that the iterative proportional fitting procedure for the construction of distributions with given multivariate marginals simplifies in the case, that the marginal system is decomposable. Decomposability of the marginal system allows to write a distribution in the marginal class as a product of conditional distributions. This property is important for the algorithmic complexity of the fitting procedure. Applications concern expert systems.

##### MSC:
 6e+06 Probability distributions: general theory
Full Text:
##### References:
 [1] I. Csiszár: $$I$$-divergence geometry of probability distributions and minimization problems. Ann. Probab. 3 (1975), 146-158. · Zbl 0318.60013 [2] W. E. Deming, F. F. Stephan: On a least square adjustment of a sampled frequency table when the expected marginal totals are known. Ann. Math. Statist. 11 (1940), 427-444. · Zbl 0024.05502 [3] A. Feinstein: Foundations of Information Theory. McGraw-Hill, New York-Toronto- London 1958. · Zbl 0082.34602 [4] R. Jiroušek: A survey of methods used in probabilistic expert system for knowledge integration. Knowledge Based Systems 3 (1990), 1, 7-12. [5] H. G. Kellerer: Verteilungsfunktionen mit gegeben Marginalverteilungen. Z. Warhsch. Verw. Gebiete 3 (1964), 247-270. · Zbl 0126.34003 [6] F. M. Malvestuto: Computing the maximum-entropy extension of given discrete probability distributions. Coraput. Statist. Data Anal. 8 (1989), 299-311. · Zbl 0726.62012 [7] Lianwen Zhang: Studies on finding hyper tree covers for hypergraphs. Working Paper No. 198, School of Business, The University of Kansas, Lawrence 1988. [8] R. E. Tarjan, M. Yannakakis: Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs. SIAM J. Comput. 13 (1984), 3, 566-579: · Zbl 0545.68062
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.