Risk assessment of rare natural hazards - such as pyroclastic flows or storm surge - is addressed. Assessment is approached through a combination of computer modeling, statistical modeling, and extreme-event probability computation. A computer model of the natural hazard is used to provide the needed extrapolation to unseen parts of the hazard space. Statistical modeling of the available data is needed to determine the initializing distribution for exercising the computer model. In dealing with rare events, direct simulations involving the computer model are prohibitively expensive. Thus an emulator – an approximation to the computer model – is developed that is capable of handling very large spatial domains and enables the computation of hazard probabilities.