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Compatibility and statistical inference for data in measurement model of Foulis and Randall. (English) Zbl 0937.05075
This paper is motivated by the work of Foulis and Randall on operational statistics; see D. J. Foulis and C. H. Randall [J. Math. Phys. 13, 1667-1675 (1972; Zbl 0287.60002)]. Let $$G=(X,E)$$ be a (possibly infinite) graph and let $$H=\bigl (X,{\mathcal E}(G)\bigr)$$ be the corresponding clique hypergraph. In the terminology of Foulis and Randall, $$H$$ is a manual of operations. The authors give a natural definition for a family of positive functions $$\mu _F\colon F\to {\mathbb{R}}^+$$, $$F\in {\mathcal E}(G)$$, to be compatible. Their main result states that $$G$$ is triangulated if and only if any compatible family of positive functions $$\mu _F$$, $$F\in {\mathcal E}(G)$$, on $$H$$ can be expressed in terms of a single (unnormed) measure on $$H$$. The authors briefly discuss some applications to experimental data and random errors.
##### MSC:
 05C99 Graph theory 05C65 Hypergraphs
##### Keywords:
graph; hypergraph; orthogonality; measure on orthogonality space
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##### References:
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