A Bayesian inference learning process for cognitive receivers is provided in this paper. We focus on the particular case of signal detection as an explanatory example to the learning framework. Under any prior state of knowledge on the communication channel, an information theoretic criterion is presented to decide on the presence of informative data in a noisy wireless MIMO communication. We detail the particular cases of knowledge, or absence of knowledge at the receiver, of the number of transmit antennas and noise power. The provided method is instrumental to provide intelligence to the receiver and gives birth to a novel Bayesian signal detector. The detector is compared to the classical power detector and provides detection performance upper bounds. Simulations corroborate the theoretical results and quantify the gain achieved using the proposed Bayesian framework.