| Authors |
Volchikhin Vladimir Ivanovich, doctor of technical sciences, professor, President of Penza State University (40 Krasnaya street, Penza, Russia), vvi@pnzgu.ru
Ivanova Nadezhda Alexandrovna, an analyst, BioCrypt LLC (9 Sovetskaya street, Penza, Russia), ivan@pniei.penza.ru
Serikova Julia Igorevna, graduate student, Penza State University (40 Krasnaya street, Penza, Russia). julia-ska@yandex.ru
Bannykh Andrey Grigoryevich, postgraduate student, Penza State University (40 Krasnaya street, Penza, Russia), ibst@pgzgu.ru
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| Abstract |
Background. The aim of the paper is to estimate the gain from using the simplest oracle, predicting the interval of uncertainty in calculating the mathematical expectation on small test samples.
Materials and methods. The algorithm for calculating the mathematical expectation has long been known and gives significant errors on small samples. This is a consequence of the fact that the classical computational algorithm does not take into account a priori information about the form of the distribution law for the values of the test sample, the size of the test sample, the mutual relationship of the experimental position in the test sample. Taking into account all these additional information parameters leads to a significant narrowing of the prediction of the interval of the possible position of the calculated mathematical expectation.
Results. It is shown that the simplest oracle constructed on the basis of the above a priori information gives a narrower range of the possible position of the mathematical expectation with a probability of 0.974. At the same time, according to his data, it is possible to determine reliably the moment when the synthesized predictor begins to err.
Conclusions. The predictor considered in this article is the simplest, presumably more complex predictors will be more difficult to customize, however, the gain from their use will be higher. Apparently, more complex predictors will be built on the basis of the use of artificial neural networks long enough for trainees to take into account the original a priori information on a large initial statistical material. The problem of transition from the simplest predictor to the synthesis of more complex neural network predictors is set.
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