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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
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References:
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