Bayesian Calculations

Abstract

Before concluding this book, we need to discuss a practical aspect of the Bayesian paradigm, namely, the computation of Bayes estimators. The ultimate simplicity of the Bayesian approach is that, given a loss function L and a prior distribution π, the Bayes estimate associated with an observation x is the (usually unique) decision d minimizing the posterior loss

$$ L\left( {\pi ,d\left| x \right.} \right) = \int_\theta {L\left( {\theta ,d} \right)\pi \left( {\theta \left| x \right.} \right)d\theta .} $$

((9.1))