Distributed peer-to-peer (P2P) applications have been gaining momentum recently. In such applications, all participants are equal peers simultaneously functioning as both clients and servers to each other. A fundamental problem is, therefore, how to select reliable servers from a vast candidate pool. To answer this important open question, we present a novel reputation system built upon the multivariate Bayesian inference theory. Our system offers a theoretically sound basis for clients to predict the reliability of candidate servers based on self-experiences and feedbacks from peers. In our system, a fine-grained quality of service (QoS) differentiation method is designed to satisfy the diverse QoS needs of individual nodes. Our reputation system is also application-independent and can simultaneously serve unlimited P2P applications of different type. Moreover, it is semi-distributed in the sense that all applicationrelated QoS information is stored across system users either in a random fashion or through a distributed hash table (DHT). In addition, we propose to leverage credits and social awareness as reliable means of seeking honest feedbacks. Furthermore, our reputation system well protects the privacy of users offering feedbacks and is secure against various attacks such as defaming, flattering, and the Sybil attack. We confirm the effectiveness and efficiency of the propose system by extensive simulation results.