Journal of Applied Mathematics and Decision Sciences
Volume 2 (1998), Issue 2, Pages 107-117
doi:10.1155/S1173912698000054
Abstract
In the classical decision theory framework, the loss is a function of the decision taken
and the state of nature as represented by a parameter θ. Information about θ can be obtained
via observation of a random variable X. In some situations however the loss will depend not
directly on θ but on the observed value of another random variable Y whose distribution depends
on θ. 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, for X and for Y, leading to a range of
behaviours in the Bayes risk. We illustrate this with a problem arising from the cleanup of sites
contaminated with radioactive waste. We also discuss some computational approaches.