A Bayesian decision theory problem is defined by a probability space , an action set , and a loss function . An element , sometimes called the ``state of nature'', represents complete knowledge relevant to the problem. Thus the loss function encodes how bad a given action would be if all the relevant problem information were available.
The Bayesian expected loss of an action is merely the expected value of the loss function for fixed .
In situations where no minimizes , there are straightforward modifications to the Conditional Bayes Principle available, such as the -Conditional Bayes Principle which states that any action within of the minimum of is acceptable.
Paul Mineiro 2001-04-18