This paper deals with the task of parameter identification using the Bayes estimation method, which makes it possible to take into account the differing consequences of positive and negative estimation errors. The calculation procedures are based on the kernel estimators technique. The final result constitutes a complete algorithm usable for specifying the value of the Bayes estimator on the basis of an experimentally obtained random sample. An elaborated method is provided for nume-rical computations. In particular, an exemplary application to a random time-optimal control for nonlinear mechanical systems is described.