  We treat the statistical inference problems in which one needs to detect and
estimate simultaneously using as small number of samples as possible.
Conventional methods treat the detection and estimation subproblems separately,
ignoring the intrinsic coupling between them. However, a joint detection and
estimation problem should be solved to maximize the overall performance. We
address the sample size concern through a sequential and Bayesian setup.
Specifically, we seek the optimum triplet of stopping time, detector, and
estimator(s) that minimizes the number of samples subject to a constraint on
the combined detection and estimation cost. A general framework for optimum
sequential joint detection and estimation is developed. The resulting optimum
detector and estimator(s) are strongly coupled with each other, proving that
the separate treatment is strictly sub-optimum. The theoretical results derived
for a quite general model are then applied to several problems with linear
quadratic Gaussian (LQG) models, including dynamic spectrum access in cognitive
radio, and state estimation in smart grid with topological uncertainty.
Numerical results corroborate the superior overall detection and estimation
performance of the proposed schemes over the conventional methods that handle
the subproblems separately.
