Decision theory is the science of making optimal decisions in the face of uncertainty. Statistical decision theory is concerned with the making of decisions when in the presence of statistical knowledge (data) which sheds light on some of the uncertainties involved in the decision problem.

Decision theory is the science of making optimal decisions in the face of uncertainty. Statistical decision theory is concerned with the making of decisions when in the presence of statistical knowledge (data) which sheds light on some of the uncertainties involved in the decision problem.$^1$

Alternatively, a general theory for the processing and use of statistical observations. In a broader interpretation of the term, statistical decision theory is the theory of choosing an optimal non-deterministic behaviour in incompletely known situations.$^2$

$^1$ Berger "Statistical Decision Theory" in Eatwell, Milgate & Newman (Eds.) "Game Theory" (1989).
$^2$ Encyclopaedia of Mathematics.