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

also the operations of various devices and systems. I also understandprediction as designing all kinds of instruments, devices, systems etc.You can say that a forecast as a demand of reproducing a publishedresult was being accepted as a definition of the final aim anddistinctive feature of natural science even at their birth.That demand apparently includes the most essential distinctionbetween natural science and magic. It should be regrettably stated thatforecasting as the final aim of the theories of natural science has partlyescaping the attention of even the scientists themselves. It seems thatthis circumstance causes the passion felt sometimes for such diffuseformulations of those goals of scientific research which are sometimesnoticeable as explanation or revealing the essence of phenomena.As an example I can cite the caustically indicated (Kitaigorodsky1978) tendency of chemists to explain a phenomenon with highprecision by introducing after the event plenty adjusting parametersinto formulas. A proper number of these can always achieve an idealcoincidence of the theoretical and the empirical curves, only not beforethe latter was experimentally obtained.Kitaigorodsky (1978) offered a formula for quantitatively indicatingthe value P of a theory: P = (k/n) − 1. Here, k is the number ofmagnitudes which can be predicted by that theory, and n, the numberof adjusting parameters. The value of a theory is therefore non-existentif k = n, and it is essential if k is much greater than n. The reader willbe certainly justified to believe that this proposal is a joke, but of akind that includes a large part of truth.A somewhat exaggerated stress on the idea of forecasting noticeablein the newest discipline (Prognostika 1975/Prognostication 1978) islikely a reaction to the mentioned partial disregard of that fundamentalidea. In this connection I indicate once more that in any concretebranch of natural science forecasting is not at all a novelty and thatduring many years a large and specific experience of forecasting hadbeen acquired with a great deal of trouble. It is hardly possible tocreate some essentially new, general and at the same time substantialtheory of forecasting. Meanwhile, however, a unification ofterminology connected with forecasting can undoubtedly play somepositive role.2. The Initial Concepts of the Applied Theory of Probability2.1. Random variables and their moments. Denote the controlledconditions of trials by U, their result by V and the magnitude measuredin trial s by X(s). The forecast of X(s + 1) given X(s) often fails.Permanence (forecast verified many times) is looked for by averagingand obtaining from initial unpredictable magnitude V 1 = X(s)V = E ( X ) = X ( s)mmwhere E m (X), in general also unpredictable, is the empirical mean of anunpredictable magnitude, of a random variable X(s). It is often stable:E m (X) ≈ E(X) (1)124