On use of predictive probabilistic estimates for selecting best decision rules in the course of a search

The problem of how to find the `best´ decision rule in the course of a search with the help of analysis of sample set is considered. Specifically the problem of selecting of best subset of regressors is highlighted. The concepts of predictive probabilistic estimate (PPE), decomposition of a search process on stages, ensemble of noise functions and reference probability distribution on it are introduced and discussed. A Monte Carlo procedure for estimating PPE is suggested and applied to a practical example. A method of obtaining upper and lower bounds for the PPE is suggested