Bayesian statistics provides a useful theoretical framework for conceptual solution of a broad range of identification problems. However, the class of numerically feasible problems is too narrow. An attempt is made to equip this theory with a systematic construction of feasible approximations applicable in real-time. The essence of the proposed solution consists in a parametric global approximation of the probabilistic system model. The problem formulation is justified, its inherent difficulties are discussed and an illustrative application to the identification of a mixture of distributions is presented.