Statistical maps. I: Basic properties (Q2777542)
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scientific article; zbMATH DE number 1717403
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Statistical maps. I: Basic properties |
scientific article; zbMATH DE number 1717403 |
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7 March 2002
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statistical map
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Markov kernel
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effect valued measure
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operational probability theory
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0.8966532
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0.88758963
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0.85323143
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0.8464709
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0.8320591
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Statistical maps. I: Basic properties (English)
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The author discusses recent results concerning statistical maps [\textit{E. Beltrametti} and \textit{S. Bugajski}, J. Math. Phys. 38, 3020--3030 (1997; Zbl 0874.06009); \textit{S. Bugajski}, Intern. J. Theor. Phys. 35, 2229--2244 (1996; Zbl 0872.60003); \textit{S. Bugajski, K.-E. Hellwig} and \textit{W. Stulpe}, Rep. Math. Phys. 41, 1--11 (1998; Zbl 1026.60501)]. A statistical map is defined to be an affine map between two simplexes of probability measures satisfying a measurability condition. The author describes the closely related concepts of Markov kernels, dual statistical maps, statistical functions and effect-valued measures. He proves that a family of statistical maps possesses a natural product that is a statistical map.NEWLINENEWLINEPart II, cf. Math. Slovaca 51, No. 3, 343--361 (2001; Zbl 1088.81022).
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