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

periodograms. It occurred that work with them can be successful forexample when adjusting systems of automatic regulation for isolatingspecific periods of disturbances so as to suppress them. The appliedtechnique is not stochastic but I considered it necessary to describebriefly the example provided by Timofeev (§ 2.3 below).Then, when becoming acquainted with some statistical medicalproblems, I encountered an apparently promising example ofapplication of multivariate analysis (§ 2.2 below). It is almostdoubtless that such methods can also be widely applied in technologyfor solving various problems of reliability of machinery. However,much efforts should be made for excluding the almost.I thought it useful to discuss also a problem of a more generalnature: what kind of aims is it reasonable to formulate for a stochasticstudy? Naturally, they should not be either too particular (that wouldbe uninteresting), or too general (unattainable), see the historicalmaterial in Chapter 1.I am sincerely grateful to the Editor, V. I. Kovalev 3 , who initiatedthis booklet and invariably helped me.1. Extreme Opinions about the Theory of Probability1.1. Laplace’s singular and very facile metaphysics. Both inteaching and during practical work I have to encounter (although evermore rarely) delusions about the actual possibilities of stochasticmethods. In an intentionally rough way they can be expressed thus.Consider some event. We are obviously unable to say whether itoccurs or not. It is therefore random, so let us study it by stochasticmethods.If you begin to argue, a few textbooks can be cited where indeed anapproximately same statement (although less roughly) is written. Itfollows that the theory of probability is a special science in whichsome essential conclusions can be made out of complete ignorance.From many viewpoints (historical, psychological, etc) it seemsinteresting to find out the historical roots of that delusion. In general,the study of the emergence of some approach (scientific approach inparticular) is extremely difficult since it usually demands an analysisof great many sources. The theory of probability was, however, luckyin some sense.At the turn of the 18 th century a greatest scholar, Laplace, summedand essentially advanced both its general ideology and concreteresults. Being extremely diligent, he left a very detailed description ofhis views and results in his Théorie analytique des probabilités (TAP).We consider it permissible to restrict our attention by analyzing thissingle source although a strict historian of science certainly will notapprove of such a view. For his part, he will be in the right; forexample, it is extremely important for the history of science to studythe evolution of Laplace’s own ideas and his relations with otherscientists, but we are actually pursuing a narrow applied aim.In our century of rapid development of the science of science weought to describe our source [see Bibliography]. It is a great volumecontaining about 58 lists 4 and it is pleasant to note that also in our time87