The predictive distribution in decision theory: acase study

[摘要] In the classical decision theory framework, the loss is a function of the decision takenand the state of nature as represented by a parameterθ. Information aboutθcan be obtainedvia observation of a random variableX. In some situations however the loss will depend notdirectly onθbut on the observed value of another random variableYwhose distribution dependsonθ. This adds an extra layer to the decision problem, and may lead to a wider choice of actions.In particular there are now two sample sizes to choose, forXand forY, leading to a range ofbehaviours in the Bayes risk. We illustrate this with a problem arising from the cleanup of sitescontaminated with radioactive waste. We also discuss some computational approaches.

[学科分类] 自然科学（综合）