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On Bayes' theorem for fuzzy data

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Abstract

There are some ideas concerning a generalization of Bayes' theorem to the situation of fuzzy data. Some of them are given in the references [1], [5], and [7]. But the proposed methods are not generalizations in the sense of the probability content of Bayes' theorem for precise data. In the present paper a generalization of Bayes' theorem to the case of fuzzy data is described which contains Bayes' theorem for precise data as a special case and allows to use the information in fuzzy data in a coherent way. Moreover a generalization of the concept of HPD-regions is explained which makes it possible to model and analyze the situation of fuzzy data. Also a generalization of the concept of predictive distributions is given in order to calculate predictive densities based on fuzzy sample information.

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References

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Authors and Affiliations

  1. Institut für Statistik und Wahrscheinlichkeitstheorie, Technische Universität Wien, Wiedner Hauptstraße 8, 1040, Wien, Austria

    R. Viertl & H. Hule

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  1. R. Viertl
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  2. H. Hule
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Viertl, R., Hule, H. On Bayes' theorem for fuzzy data. Statistical Papers 32, 115–122 (1991). https://doi.org/10.1007/BF02925485

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  • DOI: https://doi.org/10.1007/BF02925485

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