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Statistical Methods for Fuzzy Data by Reinhard Viertl

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17.1 Discrete case

For discrete stochastic quantities X ~ p(·|θ), θ ∈ Θ = {θ1,…,θm}, and sample x1,…,xn of X, the a posteriori probabilities π (θj|x1,…,xn) = are obtained as explained at the beginning of Part V.

The predictive distribution of X|x1,…,xn is given by its predictive probabilities for all xMx where Mx is the observation space of X, i.e. the set of all possible values of X.

In the case of fuzzy a posteriori distribution π*j|x1,…,xn) the so-called fuzzy predictive distribution of X|x1,…,xn is given by its fuzzy probabilities

Unnumbered Display Equation

The fuzzy a posteriori probabilities π*(θj|x1, …xn) are obtained as explained in Section 14.2.

Remark 17.1:

Observations from discrete stochastic quantities can be exact values xi, whereas observations from continuous quantities are usually fuzzy.

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