Dear BUGS users,
I posted a request about using BUGS to do Bayesian decision analyses
with a loss function. Numerous individuals asked for a summary of the
responses, so I am sending my summary to the list.
1) Chris Theobald provided the following reference:
The Bayesian choice of crop variety and fertilizer dose. CM Theobald
and M Talbot, 2002, Applied Statistics, 51, 23-36
We use a Bayesian model and a utility function for deciding between
rival varieties of a crop which is to be grown in a target environment,
and choose the optimum amount of fertilizer for the site and variety.
2) Robert Dorazion provided the following reference:
I have used BUGS in the context natural resource management.
Dorazio, R. M. and Johnson, F. A. 2003. Bayesian inference and decision
theory - a coherent framework for decision making in natural resource
management. Ecologial Applications, in press.
The article includes both theory and some
numerical illustrations using WinBugs.
The pdf file available on the web at
http://www.fcsc.usgs.gov/SEAMG/seamg_products/seamg_products.html
3) Radu Craiu responded:
For a particular loss function L(theta, d(x)) you want to calculate
E[L(theta, d(x))|x] where x is the data and d(x) is the decision you want
to use (the expectation is with respect to the posterior distribution of
theta).
You can use Bugs to draw samples from the posterior distribution of theta,
say theta_1, theta_2,....,theta_k
Then the aforementioned expectation is approximated using
sum_{i=1}^k L(theta_i,d(x))/k
I hope that this is of use to all the list members who contacted me
directly.
Thanks to all those who responded with information.
Sincerely,
Peter Austin
Peter Austin, PhD
Scientist
Institute for Clinical Evaluative Sciences
Toronto, ON
Canada
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