S.I. Melnyk

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The aprioristic information on statistical properties is necessary for using of a method of the maximum credibility based on the Bayes rule in a problem of a filtration of noise, both a useful signal, and noise. If such information on object of measurement (control) and noise cannot be formalized, as parameters of probability distribution, it is lost, as a rule. In the paper it is shown that the method of minimization of algebraic complexity of the description of the measured data is generalization of the Bayes rule on any kind information. It is shown that widely known methods of the decision of return problems of allocation of a useful signal (root-mean-square minimization, an optimum spectral filtration, etc.) it is possible to interpret, as its special cases. Illustrations of application of this method which on occasion gives improvement of accuracy of reconstruction several times are given. It is offered to consider relative complexity of the description of results of measurement and reconstructed values as the measure of their uncertainty.