Risk function


 * This article is about the mathematical definition of risk in statistical decision theory. For a more general discussion of concepts and definitions of risk, see the main article Risk.

In decision theory, the risk of an estimator &delta;(x) to be calculated from some observables x is the expected value of the loss function as a function on the unknown underlying state of nature &theta;:
 * $$ R(\theta,\delta(x)) = \int L(\theta,\delta(x)) f(x|\theta)\,dx$$.