The authors discuss problematic situations that arise in practical application of a number of mathematical constructions on the basis of statistical methods. They consider the examples that demonstrate positive role of doubt for ensuring the transition to results mathematically justified and verified by computer simulation. The authors have stated that at the present stage of science and technology development radical doubts lead to the knowledge labyrinth construction that includes interdisciplinary interaction, iteration, and search for ways out of deadlocks.

Keywords: radical doubts; statistical methods; correlation analysis; signal-noise ratio; labyrinth of knowledge.

References

1. Dekart R. Pervonachala filosofii (Principles of Philosophy), Sochineniya, v 2 t., T. 1., M., Mysl’, 1989, pp. 297—422, Filosofskoe nasledie; t. 106).
2. Istoriya filosofii (History of Philosophy), Red. V. M. Mapel’man, M., PRIOR, 1997, 464 p. 
3. Pirogov A. I. Dekart: refleksiya osnovanii nauchnogo myshleniya (Descartes: Scientific Thinking Basics’ Reflection), Ekonomicheskie i sotsial’no-gumanitarnye issledovaniya, 2015, No. 2 (6), pp. 25—26.
4. Tsypkin Ya. Z. Adaptatsiya i obuchenie v avtomaticheskikh sistemakh (Accommodation and Teach-In in Automatic Systems), M., Nauka, Gl. red. fiz.-mat. lit., 1968, 399 p., ris., tabl.
5. Middlton D. Vvedenie v statisticheskuyu teoriyu svyazi: v 2 t. (Statistical Communication Theory: in 2 Vols.), Per. s angl., pod red. B. R. Levina, M., Sovetskoe radio, 1961—1962.
6. Tsypkin Ya. Z. Osnovy teorii avtomaticheskikh system (Automatic Systems Theory Basics), M., Nauka, 1977, 560 p., il., tabl.
7. Bakhtadze N. N., Lototsky V. A. The Identification Technique with Associative Search Based Learning, Proceedings of the IX International Conference “System Identification and Control Problems” SICPRO’12, M., In-t probl. upr. im. V. A. Trapeznikova RAN, 2012, CD-ROM, pp. 16—27.
8. Troyanovskii V. M. Informatsionno-upravlyayushchie sistemy i prikladnaya teoriya sluchainykh protsessov (Information Management Systems and Applicable Theory of Random Processes), M., Gelios ARV, 2004, 304 p., il.
9. Ostanin S. A. “Uvelichenie otnosheniya signal/shum metodom posledovatel’nogo vychisleniya avtokorrelyatsionnoi funktsii” (Signal-Noise Ratio Increasing through Sequential Calculation of the Autocorrelation Function). Zhurnal radioelektroniki 12 (2011). Web. 16 May 2016. <http://jre.cplire.ru/jre/dec11/13/text.pdf>.
10. Troyanovskiy V. M., Serdyuk O. A., Zapevalina A. A. Information Technologies and Web Interfaces as a Platform for Identification of Remote Dynamic Objects, Proceedings of the Sixth International Conference on Internet Technologies and Applications (ITA), Wrexham, Glyndŵr University, 2015, pp. 323—326.