Attack graphs are a powerful tool for security risk assessment by analysing network vulnerabilities and the paths attackers can use to compromise valuable network resources. The uncertainty about the attackers behaviour and capabilities make Bayesian networks suitable to model attack graphs to perform static and dynamic analysis. Previous approaches have focused on the formalization of traditional attack graphs into a Bayesian model rather than proposing mechanisms for their analysis. In this paper we propose to use efficient algorithms to make exact inference in Bayesian attack graphs, enabling the static and dynamic network risk assessments. To support the validity of our proposed approach we have performed an extensive experimental evaluation on synthetic Bayesian attack graphs with different topologies, showing the computational advantages in terms of time and memory use of the proposed techniques when compared to existing approaches.