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O. Sunanta, R. Viertl:
"Bayesian Inference and Fuzzy Information";
Berichts-Nr. Forschungsbericht ASTAT-2016-1, Dezember, 2016; 11 S.

In standard Bayesian inference, a-priori distributions are standard probability distributions. Bayes´ theorem
formulates the transition from the a-priori distribution of the stochastic quantity, which describes the parameter of interest, to the a-posteriori distribution. However, the use of a-priori densities in form of standard probability densities has been criticized in some situations, specifically
where real observations from continuous quantities are not pr
ecise numbers, but rather non-precise (also called fuzzy).
In other words , information in form of collected data from continuous quantities is always more or less fuzzy.
Such data can be described by socalled fuzzy numbers. Moreover, in this case, a more general form of a-priori distributions (so-
called fuzzy a-priori densities) is suitable to model
a-priori information.
The combination of fuzziness and stochastic uncertainty calls for a generalization of Bayesian inference, i.e. fuzzy Bayesian inference. As a result, Bayes´ theorem has to be generalized to
handle this situation. This is possible and will be explained in
the chapter.

Characterizing Function · Generalized Bayes´ Theorem · Fuzzy Bayesian Inference · Fuzzy Data · Fuzzy Predictive D ensity

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