Sufficient statistics and reproducing densities in simultaneous sequential detection and estimation

The doubly-compound hypothesis detection problem with finite-dimensional parameter vectors is treated in a general context. It is shown that estimation and detection occur simultaneously, with the detector using the a posteriori densities generated by two separate estimators, one for each hypothesis. No assumptions are made on the estimation criterion and very loose assumptions on the detection cfiterion. If sufficient statistics and hence natural conjugate densities exist for the unknown parameters, the procedure is quite tractable. In this case, the optimal detector partitions in such a way that the primary processing can be done without knowledge of the a priori parameter distributions.