The paper considers the composite detection problem where both detection and parameter estimation are of primary interest. Based on a Neyman-Pearson type of formulation, our goal is to find the joint detector and estimator that minimizes a decision-dependent Bayesian estimation risk subject to the detection error probability constraints. The optimal joint solution not only yields lower Bayesian estimation risk compared to the conventional method, which combines the likelihood ratio test and the Bayesian estimator in sequence, but
also allows for flexible tradeoff between the detection performance and the estimation accuracy.