Introduction to Volcanic hazard
Marzocchi, W., Selva, J., and L. Sandri, Probabilistic Volcanic Hazard Assessment and Eruption Forecasting: The Bayesian Event Tree approach , in Conception, verification and application of innovative techniques to study active volcanoes, Ed. W. Marzocchi and A. Zollo, ISBN 978-88-89972-09-0, 2008.

One of the major goals of modern volcanology is to set up a sound risk-based decision making in land use planning and emergency management. Despite different scientific disciplines attribute disparate definition to the term "risk", in volcanology the most used definition reads (e.g., UNESCO, 1972; Fournier d'Albe, 1979)

risk = hazard x value x vulnerability

where hazard is the probability of any particular area being affected by a destructive volcanic event within a given period of time; the valueis the number of human lives at stake, or the capital value (land, buildings, etc.), or the productive capacity (factories, power plants, highways, etc.) exposed to the destructive events; the vulnerabilityis a measure of the proportion of the value which is likely to be lost as a result of a given event. The above equation points out that risk assessment involves different scientific expertise. As a matter of fact, any risk-based decision/action taken from authorities in charge to manage volcanic emergencies and/or risk mitigation trategies has to account also for complex inter-plays between social and economic needs, and infrastructure capability to sustain them. In particular, it is necessary to evaluate the vulnerability of exposed infrastructure, facilities and property, the impact of eruptions on human beings, costs vs. benefits of proposed mitigation measures, and the level of "acceptable risk" for society. In addition, we need educational programs to improve the "risk perception" of the people living around volcanoes, and improved ways to communicate risk and associated uncertainties to those people, mass media, and local authorities. In this compound framework, the role of volcanology is mostly focused on providing a reliable volcanic hazard assessment.

As for the term risk, also the term hazardcan lead to some misunderstanding. In English, hazardhas the generic meaning "potential source of danger", but, as mentioned before, for more than thirty years (e.g., Fournier d'Albe, 1979), hazardhas been also used in a more quantitative way, that reads: "the probability of a certain hazardous event in a specific time-space window". However,many volcanologists still use "hazard" and "volcanic hazard" in purely descriptive and subjective ways.For this reason,in order to minimize ambiguities,many researchers have recently proposed that a more suitable term for the estima- tion of quantitative hazard is "Probabilistic Volcanic Hazard Assessment" (PVHA, hereinafter; see Marzocchi et al., 2007a).

Despite the still large use of "qualitative" and "subjective" volcanic hazard assessment, PVHA has undoubtedly many pivotal advantages:

We conclude this paragraph giving emphasis to a couple of important issues. First, PVHA does not reduce in any way the importance of deterministic studies and the analysis of specific scenarios. The simultaneous use of physical models and data contrasts with what is sometimes encountered in seismic risk analysis, where deterministic and probabilistic approaches are often considered irreconcilable (e.g., Castanos and Lomnitz, 2002). In seismic hazard assessment, the terms "probabilistic" and "deterministic", contained in acronyms PSHA and DSHA, reflect the kind of strategy adopted, mostly evidence- based for PSHA and mostly based on physical models for DSHA. In volcanology, we do not see this conflict; we attempt to use all the information we have (models, data, and expert beliefs), and the term "probabilistic" in PVHA only emphasizes that the quantification of volcanic hazard takes account of associated uncertainties.

Second, we remark that the great importance of this scientific issue is due to its practical implications for society; in this perspective, no matter what probabilistic approach is used, it is fundamental that PVHA is "accurate" (i.e., without significant biases), because a biased estimation would be useless in practice. On the other hand, PVHA may have a low "precision" (i.e., a large uncertainty) that would reflect our scarce knowledge of some physical processes involved, from the preparation of an eruption to the derived impact on the ground of a specific threatening event (e.g., pyroclastic flow, lahars, etc.). An accurate PVHA can be realistically achieved by using some sort of "best picture" of the shared state-of-the-art, and by including all the existing uncertainties. This approach allows the potential bias associated to personal convictions and to lacks of knowledge to be minimized. In particular, we caution against the use of even sophisticated models that are not yet properly tested, because they certainly increase the precision, but they can introduce a significant bias making the estimation highly inaccurate.

Model BET_VH: Bayesian Evnet tree for Volcanic Hazard

In this section, we describe a possible strategy for PVHA based on Bayesian Event Tree (BET hereinafter). Basically

BET translates volcanological input into probability of any possible volcano-related event.

The "volcanological input" is every types of information relevant for the event under study. It ranges from models (i.e., ash fall model), to historical/volcanological information (i.e., eruptive catalogs), to monitoring measures (i.e., detecting magma movement), and so on... A detailed description of the procedure can be found in Marzocchi et al. (2004; 2006; 2007b), and Newhall and Hoblitt (2002). Other references on similar Bayesian strategy and,in general,on probabilistic approach are Gelman et al. (1995), Aspinall et al. (2003), Jacquet et al. (2006). Here, we report only the main features of BET that can be summarized in few general points:
For more info, please visit the BET (Bayesian Event Tree) website.