Some Remarks on Statistical Inference

Abstract

Probability and Statistics have always been highly contentious parts of science. They have been the occasion of many disputes about principles, conducted not always with cool scientific detachment and decorum. What has been disputed about is not mathematics, not pure mathematics. It is true that, from time to time, mathematicians, even eminent mathematicians, have resisted or scoffed at the introduction of new ideas or new areas of investigation in pure mathematics, for example, continuous functions without derivatives, the Lebesgue integral, and a proper treatment of the real number system, and that even today some older applied mathematicians speak of such things as abstract algebra and topology as frills. But these are merely the grumbles of old age and laziness, and they never last long. It is in the applications of mathematics, in applied mathematics, especially where experimental testing or verification is difficult, or for the time being impossible, that the violent arguments take place. Relativity in its early days is an example. In probability it is the principles governing the applications, especially in statistics, about which there are great differences of opinion.