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

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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
BibliographyAlimov Yu. I. (1976, 1977, 1978b), Elementy Teorii Eksperimenta (Elements ofthe Theory of Experiments), pts 1 – 3. Sverdlovsk.--- (1978a Russian), On the applications of the theory of probability considered inV. N. Tutubalin’s works. Avtomatika, No. 1, pp. 71 – 82.--- (1979 Russian), Once more about realism and fantasy in the applications of thetheory of probability. Ibidem, No 4, pp. 103 – 110.Anscombe F. J. (1967), Topics in the investigation of linear relations. J. Roy.Stat. Soc., vol. B 29, pp. 1 – 52.Blekhman I. I., Myshkis A. D., Panovko Ya. G. (1976), Prikladnaia Matematika(Applied Math.). Kiev.Dodge Y. (2003), Oxford Dictionary of Statistical Terms. Oxford.Grekova I. (1976 Russian), Special methodical features of applied mathematicson the current stage of its development. Voprosy Filosofii No. 6, pp. 104 – 114.Kitaigorodsky A. I. (1978), Molekuliarnye Sily (Molecular Forces). Moscow.Knut D. E. (1977 Russian), The Art of Computer Progamming, vol. 2. Moscow.The author referred to this Russian edition.Kolmogorov A. N. (1956 Russian), Theory of probability. In: Matematika. EeSoderzanie, Metody i Znachenie (Mathematics. Its Contents, Methods andImportance), vol. 2. Moscow, pp. 252 – 284.Kolmogorov A. N., Prokhorov Yu. V. (1974 Russian), Statistics. Great Sov.Enc., 3 rd ed., English version, 1977, vol. 15, pp. 721 – 725.Nikitina E. P., Freidlina V. D., Yarkho A. V. (1972), Kollekzia OpredeleniyTermina “Statistika” (Collection of Definitions of the Term “Statistics”). Moscow.Postnikov A. G. (1960), Arifmeticheskoe Modelirovanie Sluchainykh Prozessov(Arithmetical Modelling of Stochastic Processes). Moscow. Perhaps included inauthor’s Izbrannye Trudy (Sel. Works). Moscow, 2005.Prognostication (1975 Russian), Great Sov. Enc., 3 rd ed., English version, vol. 21,1978.Prokhorov Yu. V., Editor (1999), Veroiatnost i Matematicheskaia Statistika.Enziklopedia (Probability and Math. Statistics. An Enc.). Moscow.Shafer G., Vovk V. (2001), Probability and Finance. It’s Only a Game. NewYork.Tutubalin V. N. (1972), Teoria veroiatnostei (Theory of Probability). Moscow.Tutubalin V. N., Barabasheva Yu. M., Devyatkova G. N., Uger E. G. (2009Russian), Kolmogorov’s criteria and Mendel’s heredity laws. Istoriko-Matematich.Issledovania, ser. 2, No. 13/48, pp. 185 – 197.Venikov V. A. (1978), Perekhodnye Elektromekhanicheskie Prozessy vElektricheskikh Sistemakh. Moscow.Vysotsky M. (1979), Pod Znakom Integrala (Under the Sign of Integral).Moscow.Walsh J. E. (1962), Nonparametric confidence intervals and tolerance regions. In:Sarhan A. E., Greenberg B. G., Editors, Contributions to Order Statistics. New York– London, pp. 136 – 143.Wiener N. (1966 Russian), Tvorez i Robot (Creator and Robot). Moscow. Theauthor referred to this Russian edition. German: possibly Mensch undMenschenmaschine.Wilks S. S. (1962), Mathematical Statistics. New York.133
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Studies in the History of Statistic
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Introduction by CompilerI am presen
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(Lect. Notes Math., No. 1021, 1983,
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sufficiently securely that a carefu
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is energy?) from chapter 4 of Feynm
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demand to apply transfinite numbers
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for stating that Ω consists of ele
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chances to draw a more suitable apa
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Let the space of elementary events
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2.3. Independence. When desiring to
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Eξ = ∑ aipi.Our form of definiti
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absolutely precisely if the pertine
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where x is any real number. If dens
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probability can be coupled with an
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Nowadays we are sure that no indepe
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λ = λ(T)with λ(T) being actually
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(1/B n )(m − A n )instead of the
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along with ξ. For example, if ξ i
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µ( − p0) ÷np0 (1 − p0)nhas an
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distribution of the maximal term |s
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ξ (ω) + ... + ξ (ω)n1n{ω :|
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P{max ξ(t) ≥ x} = 0.01, 0 ≤ t
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1. This example and considerations
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IIV. N. TutubalinTreatment of Obser
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structure of statistical methods, d
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Suppose that we have adopted the pa
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and the variances are inversely pro
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It is interesting therefore to see
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is applied with P(t) being a polyno
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ut some mathematical tricks describ
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It is clear therefore that no speci
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of various groups of machines, and
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nnA(λ) x sin λ t, B(λ) = x cosλ
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of the mathematical model of the Br
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dF(λ) = f (λ) dλ, so that B( t
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usually very little of them. Indeed
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This is the celebrated model of aut
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applications of the theory of stoch
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achieved by differentiating because
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u(x 1 , x 2 , t 1 , t 2 ) = v(x 1 ,
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Page 85 and 86: IIIV. N. TutubalinThe Boundaries of
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Page 117 and 118: What objections can be made? First,
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Page 139 and 140: VIOscar SheyninOn the Bernoulli Law
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