We consider a well defined joint detection and parameter estimation problem.
By combining the Baysian formulation of the estimation subproblem with suitable
constraints on the detection subproblem we develop optimum one- and two-step
test for the joint detection/estimation case. The proposed combined strategies
have the very desirable characteristic to allow for the trade-off between
detection power and estimation efficiency. Our theoretical developments are
then applied to the problems of retrospective changepoint detection and MIMO
radar.