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

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Belova L. A., Mamikonianz L. G., Tutubalin V. N. (1965 Russian), Probabilityof a breakdown puncture of the insulation of the coil of turbo-generators dependingon the duration of work. Elektrichestvo, No 4, pp. 42 – 47.--- (1967 Russian), On statistical homogeneity of the insulation of the frame ofstators of turbo-generators. Elektrichestvo, No. 6, pp. 40 – 46.Box G. E. P., Jenkins G. M., Bacon D. W. (1967), Models for forecastingseasonal and non-seasonal time series. In Spectral Analysis of Time Series. NewYork, pp. 271 – 311.Box G. E. P., Jenkins G. M. (1970), Time Series Analysis, Forecasting andControl. San Francisco.Hannan E. J. (1960), Time Series Analysis. London.Ivakhnenko A. G., Lapa V. G. (1971), Predskazanie sluchainykh prozessov(Prediction of Stochastic Processes). Kiev.Jenkins G. M., Watts D. G. (1968), Spectral Analysis and Its Application. SanFrancisco, 1971.Kendall M. G. (1946), Contributions to the Study of Oscillatory Time Series.Cambridge.Kendall M. G., Stuart A. (1968), The Advanced Theory of Statistics, vol. 3.London, 1976.Matheron G. (1962), Traité de géostatistique appliquée. Paris.Monin A. S., Jaglom A. M. (1967 Russian), Statistical Fluid Mechanics.Cambridge, Mass., 1973 – 1975.Moran P. A. P. (1954), Some experiments on the prediction of sunspot numbers.J. Roy. Stat. Soc., vol. B16, pp. 112 – 117.Rytov S. M. (1966), Vvedenie v Statisticheskuiu Radiofiziku (Introduction inStatistical Radio Physics). Moscow, 1976.Slutsky E. E. (1927 Russian), Summation of random causes as the source ofcyclic processes. Econometrica, vol. 5, 1937, pp. 105 – 146.Tucker A. (1768 – 1778), The Light of Nature Pursued, vols 1 – 7. Publishedunder the name Edw. Search. Abridged edition, 1807.Wiener N. (1952), Comprehensive view of prediction theory. Proc. Intern. Congr.Mathematicians 1950. Cambridge, Mass., vol. 2, pp. 308 – 321.--- (1969), Survey of Cybernetics. London. Possible reference; author had notprovided exact source.Youshkevich A. P. (1977), On the history of the notion of function. Arch. Hist.Ex. Sci., vol. 26.Yule G. U. (1927), On a method of investigating periodicities in disturbed seriesetc. Phil. Trans. Roy. Soc., vol. A226, pp. 267 – 298.84
IIIV. N. TutubalinThe Boundaries of Applicability(Stochastic Methods and Their Possibilities)Granitsy Primenimosti(veroiatnostno-statisticheskie metody i ikh vozmoznosti).Moscow, 19771. IntroductionI have published two booklets [i, ii]. The first was devoted toelementary statistical methods, the second one, to somewhat morecomplicated methods. Their main idea was that stochastic methods(like the methods of any other science) can not be applied withoutexamination to any problem interesting for the researcher; there existdefinite boundaries of that applicability.Rather numerous comments followed, naturally positive andnegative and, as far as I know, the former prevailed. In purelyscientific matters a numerical prevalence (during some short period)can mean nothing; concerning publications, it is not so. The possibilityof reprinting [i] for a broader circle of readers had been discussed.However, considering that problem, I have gradually concluded thatduring the last five years its contents had in some specific sense, seebelow, become dated.The point is certainly not that previously stochastic methods shouldnot have been applied if the studied phenomenon was not statisticallystable, but that now it became possible. This could have happened ifnew methods not demanding that condition were developed, butscience does not advance so rapidly. However, a quite definite andprovable by referring to publications shift in the viewpoint on thesphere of applications of stochastic methods had happened. It willeventually make proving such a simple circumstance as the need torestrict somehow the application of the theory of probability almostunnecessary.Then, a rapid development of concrete statistical investigations iscertainly in the spirit of our time. They are difficult, demanding almostsuperhuman patience and insistence, but they still emerge and arebeing done. In a single statistical investigation, the study of statisticalstability is practically impossible (and at best only if the result isnegative). However, a repeated (actually, during many years)statistical investigation accompanied by checks of the conclusions onever new material provides them quite sufficient certainty.More precisely, we always come to understand what we knowcertainly; what somewhat doubtfully; and what we do not know at all.For a publication intended for a wide circle of readers it is thereforeextremely important to show how should statistical investigations becarried out from the methodical point of view so that the conclusionsare sufficiently certain for being practically applied. No generalmathematical results are here available, this can only be done byexamples.85
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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
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
Page 55 and 56: It is interesting therefore to see
Page 57 and 58: is applied with P(t) being a polyno
Page 59 and 60: ut some mathematical tricks describ
Page 61 and 62: It is clear therefore that no speci
Page 63 and 64: of various groups of machines, and
Page 65 and 66: 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
Page 83: answering that question is extremel
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
Page 115 and 116: or, for discrete observations,IT(ω
Page 117 and 118: What objections can be made? First,
Page 119 and 120: eliability and queuing are known to
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
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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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