  A vulnerability scan combined with information about a computer network can
be used to create an attack graph, a model of how the elements of a network
could be used in an attack to reach specific states or goals in the network.
These graphs can be understood probabilistically by turning them into Bayesian
attack graphs, making it possible to quantitatively analyse the security of
large networks. In the event of an attack, probabilities on the graph change
depending on the evidence discovered (e.g., by an intrusion detection system or
knowledge of a host's activity). Since such scenarios are difficult to solve
through direct computation, we discuss and compare three stochastic simulation
techniques for updating the probabilities dynamically based on the evidence and
compare their speed and accuracy. From our experiments we conclude that
likelihood weighting is most efficient for most uses. We also consider
sensitivity analysis of BAGs, to identify the most critical nodes for
protection of the network and solve the uncertainty problem in the assignment
of priors to nodes. Since sensitivity analysis can easily become
computationally expensive, we present and demonstrate an efficient sensitivity
analysis approach that exploits a quantitative relation with stochastic
inference.
