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In this letter, a novel stochastic strategy to spectrum sensing is investigated for the purpose of improving spectrum sensing efficiency of cognitive radio (CR) systems. The problem of selecting the optimal sequence of channels to finely sensing is formulated as an optimization problem to maximize the probability of obtaining available channels, and is then subsequently solved by using a Markov-Chain Monte-Carlo (MCMC) scheme. By employing a nonparametric approach such as the MCMC scheme, the reliance on specific traffic models is alleviated. Experimental results show that the proposed algorithm has the potential to achieve noticeably improved performance in terms of overhead and percentage of missed spectrum opportunities, thus making it well suited for use in CR networks.