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

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