1 Studies in the History of Statistics and Probability ... - Sheynin, Oscar

peculiar for the foundations of physics but remote from experiment.Advisable here are efficient phenomenal models without specialclaims to fundamentalism. According to the principle of equal stabilityof all the elements of an applied investigation, introduction ofcomplicated mathematics should be considered guardedly. I concludeby quoting Wiener (1966 from Russian), hardly an opponent ofmathematization:Advancement of mathematical physics caused sociologists to bejealous of the power of its methods but was hardly accompanied bytheir distinct understanding of the intellectual sources of that power.[...] Some backward nations borrowed Western clothes andparliamentary forms lacking personality and national distinctivemarks, vaguely believing as though these magic garments andceremonies will at once bring them nearer to modern culture andtechnology, − so also economists began to dress their very inexactideas in rigorous formulas of integral and differential calculuses. [...]However difficult is the selection of reliable data in physics, it is muchmore difficult to collect vast economic or sociological informationconsisting of numerous series of homogeneous data. [...] Under thesecircumstances, it is hopeless to secure too precise definitions ofmagnitudes brought into play. To attribute to such magnitudes,indeterminate in their very essence, some special precision is useless.Whatever is the excuse, application of precise formulas to these toofreely determined magnitudes is nothing but a deception, a vain wasteof time.Notes1. Both randomization and the Monte Carlo method are mentioned by Prokhorov(1999) and Dodge (2003). Tutubalin, who had sided with Alimov, later applied theMonte Carlo method in a joint contribution (Tutubalin et al 2009, p. 189). O. S.2. Concerning the theory of probability the author was likely wrong, see Tutubalin[i, § 4.2], who [i, § 4.5] also remarked that for natural science the significance of theLLN only consisted in reflecting the experimental fact of the stability of the mean.The author’s next sentence had to do with the application of the LLN to statistics, buthe only stated what that theorem did not achieve.Concerning the CLT I quote Kolmogorov (1956, p. 269): Even now, it is difficultto overestimate [its] importance. O. S.3. In spite of numerous efforts made, the Mises approach remains actuallyquestionable, see end of [vi]. O. S.4. It is worthwhile to quote another definition (Kolmogorov & Prokhorov1974/1977, p. 721):[Mathematical statistics is] the branch of mathematics devoted to themathematical methods for the systematization, analysis and use of statistical data forthe drawing of scientific and practical inferences. O. S.5. See the Introduction to [v]. O. S.6. I illustrate principal and secondary magnitudes (§ 2.6) by Kolmogorov’sreasoning. Frequency µ/n tends to probability p, and the probability P(|µ/n − p| < ε) isa secondary magnitude which in turn should be measured as well. O. S.7. This statement is not altogether correct. See Wilks (1962, Chapter 11) andWalsh (1962) who discuss non-parametric estimation and order statisticsrespectively. O. S.8. Perhaps Kolmogorov (1963). O. S.132