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In this paper, we propose a Bayesian-inference-based recommendation system for online social networks. In our system, users share their content ratings with friends. The rating similarity between a pair of friends is measured by a set of conditional probabilities derived from their mutual rating history. A user propagates a content rating query along the social network to his direct and indirect friends. Based on the query responses, a Bayesian network is constructed to infer the rating of the querying user. We develop distributed protocols that can be easily implemented in online social networks. We further propose to use Prior distribution to cope with cold start and rating sparseness. The proposed algorithm is evaluated using two different online rating data sets of real users. We show that the proposed Bayesian-inference-based recommendation is better than the existing trust-based recommendations and is comparable to Collaborative Filtering (CF) recommendation. It allows the flexible tradeoffs between recommendation quality and recommendation quantity. We further show that informative Prior distribution is indeed helpful to overcome cold start and rating sparseness.