Bayesian confidence regions
In contrast to classical confidence regions in objectivist statistics Bayesian confidence regions have an immediate probabilistic interpretation also after the sample is observed. This is by the availability of the a posteriori distribution π(·|D). A Bayesian confidence region for the parameter θ of a stochastic model X ~ f(·|θ);θ ∈ Θ and confidence level 1 – α is a subset Θ1−α of Θ for which
In the case of continuous parameter space Θ the confidence region Θ1−a is defined by
For fuzzy data D* the concept of Bayesian confidence regions has to be generalized.