  Mode {also called MAP} estimation, mean estimation and median estimation are
examined here to determine when they can be safely used to derive {posterior)
cost minimizing estimates. (These are all Bayes procedures, using the mode.
mean. or median of the posterior distribution). It is found that modal
estimation only returns cost minimizing estimates when the cost function is
0-t. If the cost function is a function of distance then mean estimation only
returns cost minimizing estimates when the cost function is squared distance
from the true value and median estimation only returns cost minimizing
estimates when the cost function ts the distance from the true value. Results
are presented on the goodness or modal estimation with non 0-t cost functions
