kniga 7 - Probability and Statistics 1 - Sheynin, Oscar

Foreword by TranslatorIn 1954, a nation-wide statistical conference was held in Moscow. It was organized by theAcademy of Sciences, the Ministry for Higher Education and the Central StatisticalDirectorate and its main aim was to seal a Marxist definition of statistics, see Kotz (1965)and Sheynin (1998, pp. 540 – 541). Below, I translate two accounts of Kolmogorov’s reportat that Conference, also see an abstract of his report at a conference in 1948 translated in thisbook.15a. Anonymous. Account of the All-Union Conference on Problems of Statistics(Extract)Moscow, 1954 (extract). Vestnik Statistiki, No. 5, 1954, pp. 39 – 95 (pp. 46 – 47)At first Kolmogorov dwells on the causes that led to the discussion of the problems ofstatistics. It became necessary, he said, in the first place, to reject sharply thosemanifestations of the abuse of mathematics in studying social phenomena that are socharacteristic of the bourgeois science. Its representatives make up, for example, differentialequations which allegedly ought to predict the course of economic phenomena; apply withoutany foundation hypotheses of stationarity and stability of time series, etc. The discussion wasalso called forth by the need to surmount in the statistical science and practice, once and forall, the mistaken aspiration of some {Soviet} statisticians to guide themselves by chaoticprocesses and phenomena 1 . And, finally, the last fact that makes the sharp discussionnecessary, Kolmogorov indicated, consists in that we have for a long time cultivated a wrongbelief in the existence, in addition to mathematical statistics and statistics as a socialeconomicscience, of something like yet another non-mathematical, although universalgeneral theory of statistics 2 which essentially comes to mathematical statistics and sometechnical methods of collecting and treating statistical data. Accordingly, mathematicalstatistics was declared a part of this general theory of statistics. Such views, also expressed atthis Conference, are wrong.It cannot be denied that there exists a certain set of methods and formulas united under thename of mathematical statistics, useful and auxiliary for each concrete science such asbiology or economics. Mathematical statistics is a mathematical science, it cannot beabolished or even made into an applied theory of probability. Not all of it is based on thistheory. The contents of mathematical statistics is described in detail in Kolmogorov’s article[2].The study of the quantitative relations in the real world, taken in their pure form, isgenerally the subject of mathematics. Therefore, all that, which is common in the statisticalmethodology of the natural and social sciences, all that which is here indifferent to thespecific character of natural or social phenomena, belongs to a section of mathematics, tomathematical statistics. […] 315b. Anonymous. On the Part of the Law of Large Numbers in Statistics (Extract)Uchenye Zapiski po Statistike, vol. 1, 1955, pp. 153 – 165 (pp. 156 – 158) …While dwelling on the law of large numbers in statistics, Kolmogorov indicates thatattempts were made in our {Soviet} literature to declare this law altogether senseless orpseudoscientific. However, considering, for the time being, indisputable examples bearing norelation to social science, the fact that this lamp remains motionless, and does not fly up tothe ceiling, is the result of the action of the law of large numbers. Air molecules moveaccording to the kinetic theory of gases with great velocities, and if their collisions were notequalized according to this law, we probably would have been unable to confer here. This