ABRAHAM WALD'S recent book, Statistical Decision Functions [10], ft presents a new theory of the foundations of statistics.'The vigorous exploration of this theory was begun by Professor Wald five or six years ago and is being continued under his leadership. Since almost all published treatments of this theory known to me, including this one, are mathematically forbidding;" and since the theory promises to be of great interest to all statisticians, it seems appropriate to attempt an informal exposition of it. The critical and philosophical remarks in this exposition may not accurately represent the views of Professor Wald, for both in writing and lecturing, he prefers to be rather noncommittal on such points.

Traditionally, the central problem of statistics is to draw statistical inferences, that is, to make reasonably secure statements on the basis of incomplete information. This entails other problems, particularly that of designing experiments which permit the strongest inference for the expenditure involved. The new theory under discussion, however, centers about the problem of statistical action rather than inference, that is, deciding on a reasonable course of action on the basis of incomplete information. There is clearly an abundance of situations calling for statistical action. Industrial quality control is a clear cut and familiar domain of examples, The problem of design evoked by the traditional inference viewpoint is also a problem of statistical action. Much more generally, it can be argued that all problems of statistics, including those of inference, are problems of action, for to utter or publish any statement is, after all, to take a certain action. Since the consequences of statements regarded as actions, especially their influences on those to whom they are directed, are often unusually difficult to analyze and appraise, for example, when the statement refers to academic science, it is well to point out that many statements, especially of applied science, are tantamount to deciding on a concrete action. Thus, medical diagnosis cannot in principle be separated from the choice of treatment. The typical agronomic experiment, though