We describe an event tree scheme to quantitatively estimate both long- and short-term volcanic hazard. The procedure is based on a Bayesian approach that produces a probability estimation of any possible event in which we are interested and can make use of all available information including theoretical models, historical and geological data, and monitoring observations. The main steps in the procedure are (1) to estimate an a priori probability distribution based upon theoretical knowledge, (2) to modify that using past data, and (3) to modify it further using current monitoring data. The scheme allows epistemic and aleatoric uncertainties to be dealt with in a formal way, through estimation of probability distributions at each node of the event tree. We then describe an application of the method to the case of Mount Vesuvius. Although the primary intent of the example is to illustrate the methodology, one result of this application merits special mention. The present emergency response plan for Mount Vesuvius is referenced to a maximum expected event (MEE), the largest out of all the possible eruptions within the next few decades. Our calculation suggest that there is a nonnegligible (1--20%) chance that the next eruption could be larger than that stipulated in the present MEE. The methodology allows all assumptions and thresholds to be clearly identified and provides a rational means for their revision if new data or information are obtained.