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

is energy?) from chapter 4 of Feynman (1963). In an excellent stylebut, regrettably in a passage too long for being quoted, it is stated therethat the law of conservation of energy can be corroborated in eachconcrete case by finding out where did energy go, but that modernphysics has no general concept of energy. This does not prevent usfrom being so sure in that law that we make a laughing-stock ofanyone telling us that in a certain case the efficiency was greater than100%. Many conclusions derived by applying stochastic methods tosome statistical ensembles are not less certain than the law ofconservation of energy.The circumstances are quite different for applying the theory ofprobability when there certainly exists no statistical ensemble or itsexistence is doubtful. In such cases modern science generally deniesthe possibility of those applications, but temptation is often strong...Let us first consider the reason why.1.2. The restrictiveness of the concept of statistical ensemble(statistical homogeneity). The reason is that that concept is ratherrestrictive. Consider the examples cited above: coin tossing, passing anexamination, rainfall. The existence of an ensemble is only doubtlessin the first of those. The business is much worse in the other twoexamples. We may discuss the probability of a successful passing ofan examination by a randomly chosen student (better, by that studentin a randomly chosen institute and discipline and examined by arandomly chosen instructor). Randomly chosen means chosen in anexperiment from a statistical ensemble of experiments. Here, however,that ensemble consists of exactly one non-reproducible experiment andwe can not consider that probability.It is possible to discuss the probability of rainfall during a givenday, 11 May, say, of a randomly chosen year, but not of its happeningin the evening today. In such a case, when considering that probabilityin the same morning, we ought to allow for all the weathercircumstances, and we certainly will not find any other day with thembeing exactly the same, for example, with the same synoptic chart, atleast during the period when meteorological observations have beenmade.Many contributions on applying the concept of stochastic processhave appeared recently. It should describe ensembles of suchexperiments whose outcome is not an event, or even a measurement(that is, not a single number), but a function, for example a path of aBrownian motion. We will not discuss the scope of that concept evenif the existence of a statistical ensemble is certain but consider theopposite case. Or, we will cite two concrete problems.The first one concerns manufacturing. We observe the value ofsome economic indicator, labour productivity, say, during a number ofyears (months, days) and wish to forecast its values. It is tempting toapply the theory of forecasting stochastic processes. However, ourexperiment only provides the observed values and is not in principlereproducible, and there is no statistical ensemble.The other problem is geological. We measured the content of auseful component in some test points of a deposit and wish todetermine its mean content, and thus the reserves if the configuration9