Long-term volcanic hazard is gaining relevance due to increasing societal demands on timescales of hundreds to hundreds of thousands of years as regards the siting for critical facilities (Chapman et al., Chapter 1, this volume). Volcanic hazard represents the probability of occurrence of a potentially damaging volcanic event within a specific period of time in a given region (UNDRO, 1979). For sites near volcanically active regions, longterm volcanic hazards often constitute the dominant source of uncertainty as input for risk assessments. Uncertainty is mainly related to imperfect knowledge of non-linear volcanic processes, to space-time variability of the distribution and intensity for volcanic events and to a limited amount of monitoring information. For these reasons the estimation of volcanic hazard is based on a probabilistic formalism (Sparks, 2003; Sparks and Aspinall, 2004).

Stochastic models have been developed in connection with the proposed high-level radioactive waste (HLW) repository at the Yucca Mountain site (Nevada, USA) in the vicinity of a Quaternary volcanic field to assess the potential for a repository disruption due to basaltic volcanism (Perry et al., 2000). The simplest approach for the estimation of volcanic hazard used a homogeneous Poisson model (Crowe et al., 1982) under the assumption of complete spatial and temporal randomness of the events. A non-homogeneous Weibull- Poisson model applied by Ho (1991) at Yucca Mountain made it possible to estimate the recurrence rate of new volcanoes being formed as a function of time.