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

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d’être consists in obtaining comparatively simple stochasticdistributions possibly describing some real phenomena 28 .Turning to reality always refreshes whereas severing theconnections with it spells danger of a scholastic degeneration.Mathematics is wonderful, but at the hands of its separaterepresentatives it can degenerate, for example into scholasticism. It isregrettably sufficiently easy to overstep the limits beyond whichbegins scholasticism. Internal problems strongly attract. A man alwayswishes to tidy his own home both because it is his home and because itis the easiest. So where is that dangerous limit overstepping which wewill only be floor polishing in our own apartment without providinganything for the society? That limit is only well seen in a historicalperspective, but at each moment it is extremely indefinite andunsteady.In a strange way statistics can partly help here, this time assumingthe aspect of science of science (Nalimov et al 1969). Rather recently acomparatively simple method was applied. It consisted of a formalstudy of the bibliographies appended to each scientific paper. Thenumber of those interested in a given circle of problems can beroughly estimated by perceiving which groups of authors quote eachother. Attempts to build up some system of administrative estimates bybasing yourself on such studies will certainly cause all the authors tocite each other in a purely formal way; and it is practically impossibleto distinguish whether references were essentially needed or includedas a payback.However, without any administrative pressure the study ofreferences is a valuable and more or less objective method of scienceof science. And such analysis shows that in probability theory onlyvery small (as compared, for example, with physics) groups of authorsrefer to each other. This means that the interest has narrowed whichwas largely caused by its unwieldy mathematical machinery and whichis a typical sign of a scholastic degeneration.Perhaps the simplest way to combat that danger is to turn to physicalapplications. Their seriousness was never doubted by anyone, and herethe interest now concentrates in particular around the problems ofstatistical physics. Most wide and complicated mathematical arsenalable to satisfy various tastes is applied. Physical problems are alsointeresting in that very much can be done by mathematical means.However, much more variable is the field of so to say purelystatistical applications. In very many important matters a far reachingmathematical analysis is impossible, but if a vast statistical materialcan be available, it can compensate to a necessary extent the scarcityof theoretical ideas. In all such cases statistical treatment is one of themain means of study. Here, I provided examples of exactly that kindabsolutely leaving aside the doubtless problem of physicalapplications.In purely statistical problems the main part is played by somestochastic model of the phenomenon. In the simplest case the supposedkind of distributions of the observations (normal, exponential,Weibull, etc) can be understood as the model. In more complicatedcases the model gets more complicated as well; the theories of118
eliability and queuing are known to apply rather complicatedanalytical models. A certain disproportion in the current developmentof probability theory consists in that a rather large number oftheoretical models (even analytically studied to a sufficient extent) iscollected, but at the same time in many cases they were neverpractically compared with reality. Of course, a creation of a theoreticalmodel marks a necessary initial period without which no suchcomparison, and no understanding of the actual data is at all possible.However, too often a study stops at that period. At the same time, eachcomparison with reality usually calls into being new models, that is,acts refreshing in that sense as well.Figures and TablesI did not reproduce them. Fig. 1 − 3 and Tables 1 and 2 concernedthe papers of Ermolaeva (1939) and Enin (1939). Tables 3 and 4 from§ 3.2 explained the Framingham experiment. Table 3 provided theexpected and actual number of taken ill, in each expected interval ofrisk, separately for men and women. Table 4 showed the estimates ofthe coefficients of the factors of risk.Notes1. See [i, Note 4]. O. S.2. This was a feature of Soviet publications (perhaps of Russian papers even now).The late Professor Truesdell told me that he was unable to read them in translation(also because translations are usually quite formal. O. S.3. Strangely enough, no editor is mentioned in the booklet. O. S.4. A list is 24 pages typescript or 16 pages of published text. O. S.5. No wonder Laplace was elected member of the French Academy (not to beconfused with the Paris Academy whose member he also was) devoted to the studyof the French language. O. S.6. Some scientists (Chebyshev, Markov) did not have any superstructure. O. S.7. The author referred (not in all necessary cases) to the text of the TAP aspublished in 1886. Instead, I provided references to its English translation(2005/2009). O. S.8. This is my quotation from Laplace (2005/2009, p. 97) inserted instead of theauthor’s description. O. S.9. There are mistakes. One of them, noticed by Pearson, concerned his model ofbirths and deaths, see Sheynin (1976, p. 160). Then, he had been keeping to his ownpractically useless theory of errors and thus caused French authors to shun Gauss(Sheynin 1977, pp. 52 – 54). Laplace’s astonishing mistake (1796/1884, p. 504) wasto state that the planets moved along elliptical paths not in accordance with Newton’sdiscovery, but because of small differences in densities and in temperatures of theirvarious parts. O. S.10. Concerning the precision of his estimate, Laplace (2005/2009, pp. 46 – 47)stated: after a century of new observations [...] examined in the same way [...]. Seealso Cournot (1843, § 137). O. S.11. Once more, see [i, Note 4]. O. S.12. See Note 10. O. S.13. The classical set-theoretic axiomatization is thus called the first one.Gnedenko (1969, p. 118), in a brief survey of the history of this problem, named onlyone pertinent publication, Lomnicki (1923). O. S.14. Concerning Ville see, for example, Shafer & Vovk (2001, pp. 48 – 50). Theother reference is Postnikov (1960) O. S.15. I have found this translation in Google with a reference to a commentator ofPlanck. O. S.16. Surely Tolstoi knew about such most actively working scholars as for exampleMendeleev or Chebyshev. O. S.119
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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
Page 67 and 68: of the mathematical model of the Br
Page 69 and 70: dF(λ) = f (λ) dλ, so that B( t
Page 71 and 72: usually very little of them. Indeed
Page 73 and 74: This is the celebrated model of aut
Page 75 and 76: applications of the theory of stoch
Page 77 and 78: achieved by differentiating because
Page 79 and 80: u(x 1 , x 2 , t 1 , t 2 ) = v(x 1 ,
Page 81 and 82: Reasoning based on common sense and
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Page 85 and 86: IIIV. N. TutubalinThe Boundaries of
Page 87 and 88: periodograms. It occurred that work
Page 89 and 90: at point x = 1. However, preceding
Page 91 and 92: He concludes that since the action
Page 93 and 94: The verification of the truth of a
Page 95 and 96: In the purely scientific sense this
Page 97 and 98: ought to learn at once the simple t
Page 99 and 100: the material world science had inde
Page 101 and 102: values of (2.1) realized in the n e
Page 103 and 104: *several dozen. The totality µ ica
Page 105 and 106: Mendelian laws. It is not sufficien
Page 107 and 108: example, the problem of the objecti
Page 109 and 110: a linear function is not restricted
Page 111 and 112: 258 - 82 - 176 cases or 68.5% of al
Page 113 and 114: The Framingham investigation indeed
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Page 117: What objections can be made? First,
Page 121 and 122: Kolman E. (1939 Russian), Perversio
Page 123 and 124: measurement is provided. Recently,
Page 125 and 126: which means that sooner or later th
Page 127 and 128: The foundations of the Mises approa
Page 129 and 130: A rather subtle arsenal is develope
Page 131 and 132: 4.3. General remarks on §§ 4.1 an
Page 133 and 134: BibliographyAlimov Yu. I. (1976, 19
Page 135 and 136: processes are now going on in the s
Page 137 and 138: obtaining a deviation from the theo
Page 139 and 140: VIOscar SheyninOn the Bernoulli Law
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1 Studies in the History of Statistics and Probability ... - Sheynin, Oscar

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