Probabilistic graphical models are very efficient modeling and reasoning tools. In this paper, we propose an efficient and novel Bayesian network model for a major problem in alert correlation which plays a crucial role in nowadays computer security. Indeed, the use of multiple intrusion detection systems (IDSs) and complementary approaches is fundamental to improve the overall detection rates. This however inevitably rises huge amounts of alerts most of which are redundant and false alarms making the manual analysis of all the amounts of triggered alerts intractable. In this paper, we first propose a Bayesian network-based model allowing to handle the reliability of IDSs when predicting severe attacks by correlating the alerts reported by the IDSs monitoring the network. Then we propose a flexible and efficient approach especially designed to limit the false alarm rates by controlling the confidence of the prediction model. Finally, we provide experimental studies carried out on a real and representative alert corpus showing significant improvements regarding the tradeoffs between the prediction rates and the corresponding false alarm ones.