7. Probability and Statistics Soviet Essays - Sheynin, Oscar

foreign scientists and are being continued. This year the Moscow collective began working{cf. below} on another urgent issue of modern mathematical statistics, on the so-calledprinciple of maximum likelihood. If adequately developed, this promises to become a mostpowerful tool for testing hypotheses and thus to foster the solution of a most importantproblem of applied statistics all the previous approaches to which did not yet for variousreasons satisfy the researchers. This work is, however, only planned.[6] I have already mentioned a number of studies done by the Moscow school andconnected with theoretical physics. For a long time now, a number of branches of biology(genetics, natural selection, struggle for existence) have been resting on stochastic methods.Even before the Revolution Bernstein developed a number of stochastic applications togenetics. Its mathematical requirements grown during the last years have demanded new,more subtle stochastic studies which the Moscow school did not take up. Glivenko, withKolmogorov participating, developed a peculiar genetic algebra. They, as well as Petrovskyand Piskunov, investigated various issues in natural selection and struggle for existence.In the sphere of technical applications of probability, the most complicated nowadays arethe problems arising in connection with the running of systems designed for general use; and,from among these, the estimation of the {necessary} equipment of telephone exchanges andnetworks. In this direction the Moscow school had studied a number of problems both ofgeneral theoretic and directly applied nature. Khinchin constructed a general mathematicaltheory of stationary queues whose particular cases are both the telephony (see just above) andthe estimation of the time passing between a machine tool, etc goes out of service and itsrepair. And he, together with Bavli, developed in the practical sense the urgent theory ofshared telephone lines and made a number of calculations directly required by the Ministry ofCommunications. All this work was carried out while keeping in constant touch withpractical specialists, engineers at the Ministry’s research institute. Finally, a specialcommission of mathematicians and engineers headed by Slutsky aims at systematicallydeveloping statistical problems arising in technology. It is now working regularly, but I oughtto remark that until now it is still restricting its efforts to gathering information and did notcompile any plans for active operations.This far from complete list of works on probability theory accomplished by the school ofthe Moscow University is sufficiently convincing and shows the range of the school’sactivities. An attentive collective discussion of all the works being carries out from theirinitiation onwards; regular ties with practical specialists and natural scientists with respect toall the applied issues; intimate contacts with all prominent scientists including foreignersconcerning all the parallel and related studies; a speedy publication of results; and effortsdirected at disseminating these among all the interested scientific circles, – none of thesefeatures of managing scientific work were, or could have been known to the prerevolutionarytheory of probability.[7] The works of Bernstein and the Moscow school do not, however, exhaust theaccomplishments of the Soviet theory of probability. The third prominent center of creativework in this field is Tashkent. The leader of mathematicians at Sredneaziatsky {CentralAsian} University, Romanovsky, is a most oustanding world authority on mathematicalstatistics. Whereas Bernstein and his associates and the Moscow stochastic school mainlyconcentrated their efforts on the theory of probability, the entire scientific world ofmathematical statistics is attentively following the work issuing from the Soviet Central Asia.It is rather difficult and unnecessary to draw a clear boundary line between the twoabovementioned sciences, but the border is mainly determined by the fact that probabilitytheory is mostly interested in theoretical regularities of mass phenomena whereasmathematical statistics creates practical methods for scientifically mastering these