Frequency Interpretations in Probability

Abstract

THE letter of mine quoted by Dr. W. E. Deming¹ was mostly in the nature of a personal explanation. I have never denied that frequencies may be relevant to a prior probability; what I deny is that a frequency is ever the whole content of a probability, whether prior, direct or posterior. I have, in fact, pointed out that prior probabilities should be reassessed from time to time to allow for accumulation of information from analogous problems, and the case considered by Deming is an extreme one of this type, since the balls in his box are derived from a large population the composition of which is definitely known. The kind of distinction involved seems to have been noticed by Laplace, if one compares his opening remarks with those of De Moivre. De Moivre begins by defining a probability as simply the ratio of the number of favourable cases to the whole number of possible cases. Laplace puts in the proviso “provided that all the cases are equally possible”; otherwise his statement is practically a translation of De Moivre's.