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

In the purely scientific sense this conclusion is not at all new. Wesaw how careful was Laplace concerning those stochastic applicationswhere indeed such carefulness was needed. Poisson, although hiscontribution on the probabilities of judicial verdicts was wrong on thewhole 11 , perfectly well understood the need to verify a number ofassumptions by factual materials and performed some checksobtaining an excellent fit [i]. And in general there was likely noresearcher who did not somehow choose to solve such problems wherethe application of the theory of probability could have provedeffective.So the discussion can only concern methodical problems (methodsof teaching). What should be included in textbooks intended forbeginners, or in a paper designed for being widely debated? Suchconsiderations lead to a special kind of reasoning that I am indeedcalling speculative criticism of the theory of probability.A student, beginning to study a subject usually does not master anyconcrete material. This concerns not only students of purelymathematical specialities for which the curriculum does not envisageany such material, but also those following applied specialities whostudy the theory of probabilities (together with all theoreticaldisciplines) during their first years of learning. If, however, weconsider a paper discussing problems of principle, it is addressed topeople who are mostly acquainted with factual materials, althoughdifferent from one of them to another. This is indeed what demands aspeculative discussion of the problem.Such discussions are based on a single principle: since the necessityof restrictions in applications of the theory of probability isacknowledged, let us see whether we are able to verify their realizationin practice. It is easily established that the restrictions are generallyformulated too indefinitely, and if desiring to check the conclusionsrather than the restrictions, we find that an exhausting verification ishere also impossible.Pertinent examples can be seen in [i] and Tutubalin (1972).However, some contributions of Alimov have become recently known.His style is very vivid, and many quotations of his statements isdesirable, but we have to choose only one (1974, p. 21):Thus, the correctness of comparing n measurements with nindependent random variables is not threatened by any experimentalcheck. Following an established tradition, such comparisons areassumed as a basis of many branches of mathematical statistics, of thetheory of Monte Carlo methods, random searching, rationalization ofexperiments and a number of other apparently serious disciplines.Being impossible to check experimentally, they are significantly, so tosay, present at the development of systems of automatic control.Here, Alimov bears in mind that, having one sample, it is impossibleto verify either the independence of separate observations or thecoincidence of their laws of distribution. In general, imagining anensemble of many possible samples given one really observable, is forhim inadmissible. Accordingly, he proposes to abandon the main95