Posterior Risk

Definition

$\rho (\pi ,\delta )=E_{\theta }[L(\theta ,\delta (x))|X=x]=\int L(\theta ,\delta (x))p(\theta |x)d\theta$

where $L(\theta ,\delta )$ is Loss Function, $R(\theta ,\delta )$ is Risk Function, and $p(\theta |x)$ is a posterior probability