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In this paper, the problem of multiantenna spectrum sensing in cognitive radio (CR) is addressed within a Bayesian framework. Unlike previous works, our Bayesian model places priors directly on the spatial covariance matrices under both hypotheses, as well as on the probability of channel occupancy. Specifically, we use inverse-gamma and complex inverse-Wishart distributions as conjugate priors for the null and alternative hypotheses, respectively; and a Bernoulli distribution as the prior for channel occupancy. At each sensing period, Bayesian inference is applied and the posterior of channel occupancy is thresholded for detection. After a suitable approximation, the posteriors are employed as priors for the next sensing frame, which can be beneficial in slowly time-varying environments. By means of simulations, the proposed detector is shown to outperform the Generalized Likelihood Ratio Test (GLRT) detector.