Method of critical variances as analytical tool of theory of inductive modeling

We stated the problem of inductive construction of noise-immune models or models with minimal error variance of extraction and prediction of exact (nonnoisy) signal. The method of critical variances, which are measure of relative efficiency of models of different complexity, is the analytical technique. The method makes it possible to investigate analytically regularities of variation of complexity of optimal structures depending on noise level, sampling length and other indexes of incompleteness of a priori information, as well as to obtain comparative estimates for efficiency of different criteria of model quality.