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In this paper, we present a unifying framework for distributed detection with dependent or independent observations. This novel framework utilizes an expanded hierarchical model by introducing a hidden variable. Facilitated by this new framework, we identify several classes of distributed detection problems with conditionally dependent observations whose optimal sensor signaling structure resembles that of the independent case. These classes of problems exhibit a decoupling effect on the form of the optimal local decision rules, much in the same way as the conditionally independent case using both the Bayesian and the Neyman-Pearson criteria.