The Long-Run Consequence of Behavior

Abstract

As a consequence of Wald’s (1950) powerful work, statistics was for a time defined as the art and science of making decisions in the face of uncertainty. The decision problem assumes the questionable true value model of Section 8.1 and contemplates deciding, on the basis of data, between various possible actions when the state of nature is unknown. It is anticipated that the data will be helpful in choosing an action since the probabilities of data depend on the state. The task of the decision maker is to choose a decision rule specifying the action d(y) to be taken if data y is observed. The theory assumes known numerical losses l (a, θ) in taking each action a when each state θ “obtains.”