Hybrid Bayesian network algorithm based on MCMC and subset simulation for reliability analysis

Infrastructure networks are central to the functioning of modern societies. Because of their spatially distributed nature, they are susceptible to large-scale natural hazard events. In the direct aftermath of a hazard it is of paramount importance to allocate the available resources in an optimal manner. Decision support systems based on probabilistic models can help in doing so. Bayesian networks represent a probabilistic modeling tool that allows combining the hazard model with the system model and they allow for Bayesian updating with new information. Exact inference is available for discrete Bayesian networks. However due to computational issues the size of the infrastructure system that can be handled by these algorithms is limited. Approximate inference through Gibbs sampling can be used as an alternative to exact inference to overcome this limitation. Inherently, Gibbs sampling is inefficient for estimating small system failure probabilities i.e. since this requires a large number of samples. To overcome this issue, we proposed to combine Gibbs sampling for Bayesian networks with subset simulation, an efficient sampling technique for estimating small failure probabilities. In this paper we apply this inference technique to a road network that is subjected to earthquakes. In this context we also show how classical component importance measures can be estimated from the samples, obtained in the course of inference.