In the Bayesian approach to decision theory, the observed x\,\! is considered fixed. Whereas the frequentist approach (i.e., risk) averages over possible samples x \in \mathcal{X}\,\!, the Bayesian would fix the observed sample x\,\! and average over hypotheses \theta \in \Theta\,\!. Thus, the Bayesian approach is to consider for our observed x\,\! the expected loss
