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.