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

measurement is provided. Recently, physicists have sometimes begunto indicate instead the mean square error of measuring the last digits ofthe experimental result, usually in brackets; for example, the velocityof light in vacuum is [...]. Essential here is that unlike confidenceprobabilities of mathematical statistics, the maximal and the meansquare error were actually measured.For many years, mathematical statistics has been activelypropagandized, but still perhaps even nowadays physicists will beunable to refrain from smiling had we told them, say, that after treatingthe observations of the velocity of light, c, according to theprescriptions of mathematical statistics, c is situated in such-and-suchconfidence interval with confidence probability P = 0.99 and within amore narrow interval with P = 0.95.I also refer to physicists in the sequel. It was in physics that thebasis of modern exact natural science had been laid, the largest amountof experience of complicated and subtle experimentation accumulatedand a developed culture of a sound treatment of experimental data hadbeen achieved. On the other hand, it was physics that provided theexample of applying mathematical structures which is now oftenrecognized not favourably enough for other fundamental and applieddisciplines. I return to that problem at the end of my booklet.Its main aim is to describe the principles of such a treatment of datathat abstains from mentioning confidence probabilities. Theseprinciples had appeared even before mathematical statistics had;indeed, appeared at the same time as the first quantitative experimentalresults in natural science did. However, they were reflected in thetheory of probability only much later during the process of thedevelopment of the approach connected with Mises. This approach hasbeen vividly discussed for decades, see my papers and textbooks(1976, 1977, 1987b; 1978a; 1979).The connection of that Mises approach with the principles andmethods different from those of mathematical statistics is fundamentaland the contents of this booklet is therefore largely reduced to aconsistent although only understandably sketchy description of thatapproach. Such an exposition is still lacking in the literature easilyread by a broad circle of readers.I am concentrating on the problems of interpretation and practicalapplication of stochastic notions. Unlike the solution of purelymathematical issues, any answers to such problems are always to alarge extent arguable and the reader ought to take it into account. I amdescribing an approach noticeably different from that of the standardtreatises and most works on probability theory and mathematicalstatistics and I repeat that my point of view is not at all new. Itsextreme version is nicely expressed, for example, by Anscombe [1967,p. 3 note]: it is inadmissible to identify statistics with the grotesquephenomenon generally known as mathematical statistics.1. Introductory Remarks about ForecastingThe final aim of research in both fundamental and applied naturalscience is a reliable forecast of the results of future experiments. Byexperiment I mean not only investigative, reconnaissance trials, but123