Bayesian Calculations

Abstract

The contraption began to quiver, steam hissing out from two or three places. The hiss grew to a shriek, and the thing began trembling. It groaned ominously. The shriek became ear-piercing. It shook so hard the table moved. The balding man threw himself at the table, fumbling a plug loose on the largest cylinder. Steam rushed out in a cloud, and the thing went still. Robert Jordan, Lord of Chaos, Book VI of the Wheel of Time. 6.1 Implementation difficulties At this stage of the book, we need to discuss a practical aspect of the Bayesian paradigm, namely, the computation of Bayes estimators. The ul-timate simplicity of the Bayesian approach is that, given a loss function L and a prior distribution π, the Bayes estimate associated with an observa-tion x is the (usually unique) decision d minimizing the posterior loss L(π, d|x) =