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In this paper, we present a probabilistic inference approach for cooperative spectrum sensing. We probabilistically model the cooperative sensing system on a representative factor graph, and approach the decision fusion problem as one of probabilistic inference on a factor graph that can be tackled by message passing algorithms like belief propagation. This approach allows for the rigorous modeling of all unknown quantities, such as channel effects, and correlations among random variables in the cooperative sensing system. Using belief propagation, we compute the likelihoods of the null and alternative hypotheses based on all observations at the fusion center, and apply the likelihood ratio test (LRT) based on the Neyman-Pearson (NP) theorem for optimal decision making. Unlike most studies in this field, we consider non-ideal transmission channels between secondary users and fusion center, as well as the presence of fading in links between primary and secondary users. We apply the proposed approach for both hard and soft local decisions and through simulation results illustrate the performance improvement achieved by the proposed NP-based LRT cooperative sensing scheme. A useful side result is that the well-known M-out-of-K collaborative sensing method is shown to be optimal for identical independent channels from the primary transmitter to each secondary user, and from each secondary user to the fusion center.