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Statistical Methods for Fuzzy Data by Reinhard Viertl

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17

Fuzzy predictive distributions

Let X ~ Pθ;θ ∈ Θ be a stochastic model with a priori distribution π(·). Then in standard Bayesian inference the predictive distribution of X, given observed data D, is denoted by X|D.

There are three practically important situations for predictions:

  • discrete X and discrete Θ;
  • discrete X and continuous Θ;
  • continuous X and continuous Θ.

For the standard situation predictive distributions conditional on observed samples D = (x1,…,xn) are available.

In the case of fuzzy a priori distributions and fuzzy samples (x1*…, xn*) of X the concept of predictive distributions has to be generalized.

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