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

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those who applies it ... The booklet is intended for a much betterqualified readership. He indicates the weak points of the attempts toapply probability theory, but his positive recommendations are notsufficiently isolated from the context and the exposition is not at allconducive for easy reading. I only translated parts of his booklet anddescribed much in my own words.Alimov’s criticism of the usual practical aspect of appliedmathematical statistics is much more radical than Tutubalin’s, sufficeit to mention the title of his contribution [iv], and he also overenthusiasticallyrejected many chapters of that discipline.A special comment is warranted by the authors’ separation of twounderstanding of randomness, its narrow mathematical meaning andits more general scientific understanding. This latter is still important;its beginning can be traced to Poincaré (1896/1912, p. 4) whoindicated that a very small cause can have a considerable effect whichwas his main explanation of randomness. His idea (effectivelypronounced earlier by several scholars including Maxwell and even byAristotle) was greatly generalized in the studies of chaotic phenomenawhich began several decades ago. I provide an example illustrating amistake made by imagining mathematical randomness instead ofrandomness in the general sense (or even simply indefiniteness).William Herschel (1817/1912, p. 579) formulated a statement aboutthe size of the stars. Not knowing anything about it or about theexistence of different spectral classes, he presumed that a starrandomly chosen from more than 14 thousand stars of the first sevenmagnitudes, is not likely to differ much from a certain mean size ofthem all. Actually, the size of the stars differ enormously and a meansize is only a purely abstract notion.Here now is Tutubalin’s explanation of February 2011.Philosophers of science had successfully proved that neither theorynor experiment were of any consequence in science and were notsuited for anything. The only possible explanation is that scientificcognition, just like religious cognition, is a miracle and revelation. Iprovided a hint of theology of science in my paper in UspekhiFizicheskikh Nauk vol. 163, No. 7, 1993, pp. 93 – 109.If you will not colour theologically your investigations, they will notgive rise to such interest as they really deserve.Perhaps most extraordinary events do happen (with an extremelylow probability). But suppose that a mathematician had somehowdivined the yet unknown Pythagorean proposition. Even then he stillhas to justify it. At first, he can draw a right triangle, measure its sidesetc, then rigorously consider his task.After reading Tutubalin’s paper mentioned above, I am still unableto say anything else on this subject, but I saw a significant statementon p. 98: for two hundred years no progress was made about thefundamental problem: when does statistical stability emerge?I have now found a highly relevant statement by Kolmogorov in theRussian translation of 1986 of his Logical foundations of probability4
(Lect. Notes Math., No. 1021, 1983, pp. 1 – 5): Randomness in thewide sense indicates phenomena which do not exhibit regularities, donot necessarily obey any stochastic laws. It should be distinguishedfrom stochastic randomness, a subject of the theory of probability.BibliographyGrekova I. (1976 Russian), Peculiar methodological features of appliedmathematics on the current stage of its development. Voprosy Filosofii, No. 6, pp.104 – 114.Fourier J. B. J. (1829), Historical Eloge of the Marquis De Laplace. London,Endinb. and Dublin Phil. Mag., ser. 2, vol. 6, pp. 370 – 381. The original French textwas only published in 1831.Herschel W. (1817), Astronomical observations and experiments tending toinvestigate the local arrangement of celestial bodies in space. Scient. Papers, vol. 2.London, 1912, pp. 575 – 591. Reprint of book: London, 2003.Poincaré H. (1896), Calcul des probabilités. Paris, 1912; reprinted 1923.5
Page 1 and 2: Studies in the History of Statistic
Page 3: Introduction by CompilerI am presen
Page 7 and 8: sufficiently securely that a carefu
Page 9 and 10: is energy?) from chapter 4 of Feynm
Page 11 and 12: demand to apply transfinite numbers
Page 13 and 14: for stating that Ω consists of ele
Page 15 and 16: chances to draw a more suitable apa
Page 17 and 18: Let the space of elementary events
Page 19 and 20: 2.3. Independence. When desiring to
Page 21 and 22: Eξ = ∑ aipi.Our form of definiti
Page 23 and 24: absolutely precisely if the pertine
Page 25 and 26: where x is any real number. If dens
Page 27 and 28: probability can be coupled with an
Page 29 and 30: Nowadays we are sure that no indepe
Page 31 and 32: λ = λ(T)with λ(T) being actually
Page 33 and 34: (1/B n )(m − A n )instead of the
Page 35 and 36: along with ξ. For example, if ξ i
Page 37 and 38: µ( − p0) ÷np0 (1 − p0)nhas an
Page 39 and 40: distribution of the maximal term |s
Page 41 and 42: ξ (ω) + ... + ξ (ω)n1n{ω :|
Page 43 and 44: P{max ξ(t) ≥ x} = 0.01, 0 ≤ t
Page 45 and 46: 1. This example and considerations
Page 47 and 48: IIV. N. TutubalinTreatment of Obser
Page 49 and 50: structure of statistical methods, d
Page 51 and 52: Suppose that we have adopted the pa
Page 53 and 54: 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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Reasoning based on common sense and
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answering that question is extremel
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IIIV. N. TutubalinThe Boundaries of
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periodograms. It occurred that work
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at point x = 1. However, preceding
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He concludes that since the action
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The verification of the truth of a
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In the purely scientific sense this
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ought to learn at once the simple t
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the material world science had inde
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values of (2.1) realized in the n e
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*several dozen. The totality µ ica
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Mendelian laws. It is not sufficien
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example, the problem of the objecti
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a linear function is not restricted
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258 - 82 - 176 cases or 68.5% of al
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The Framingham investigation indeed
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or, for discrete observations,IT(ω
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What objections can be made? First,
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eliability and queuing are known to
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Kolman E. (1939 Russian), Perversio
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measurement is provided. Recently,
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which means that sooner or later th
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The foundations of the Mises approa
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A rather subtle arsenal is develope
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4.3. General remarks on §§ 4.1 an
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BibliographyAlimov Yu. I. (1976, 19
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processes are now going on in the s
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obtaining a deviation from the theo
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VIOscar SheyninOn the Bernoulli Law
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1 Studies in the History of Statistics and Probability ... - Sheynin, Oscar

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