Bayes estimates under asymmetric loss

Bayes estimates under asymmetric loss are studied. Auxiliary results for asymmetric loss functions are derived. Examples of asymmetric loss functions are considered, and the resulting Bayes estimates differing from the posterior mean are given. The introduction of an asymmetric loss function with an asymmetric parameter gives additional possibilities to account for overestimation or underestimation. For practical applications, one value for a parameter can be treated more easily than a credibility interval. This Bayes estimate differs from the posterior mean in the direction of smaller increase of loss. Thus, an expedient of many engineers, correcting for values to the secure side, is formalized using Bayes methods.>