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Journal of Applied Mathematics and Decision Sciences
Volume 2 (1998), Issue 2, Pages 107-117

The predictive distribution in decision theory: a case study

Institute of Information Sciences and Technology, College of Sciences, Massey University, New Zealand

Copyright © 1998 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.