Disasters are large intractable problems that test the ability of communities and nations to effectively protect their populations and infrastructure, to reduce both human and property loss, and to rapidly recover. The randomness of impacts and problems, and uniqueness of incidents demand dynamic, real-time, effective and cost efficient solutions. For this reason, we need quantitative risk-based methods for decision-making under uncertainty to be developed and applied to volcanology. Volcanic activity is a natural phenomenon that can turn into a disaster under certain conditions. They are natural processes that cannot be controlled, but their potentially disastrous effects can be mitigated. Volcanoes have implicit a natural hazard which can threaten human lives and properties of those communities living near by. The eruptions of volcanoes considered "dormant" or "inactive" have been liable for major disasters in the past. The volcanic hazard from volcanoes with a long term recurrence tends to be ignored, especially when little or no historical data exists. This is the case of Teide - Pico Viejo Stratovolcanoes in the island of Tenerife. Due to the limited scientific observability of the interior of a volcano, there is a lot of uncertainty in forecasting volcanic eruptions. During a volcanic crisis decision-makers need to take important life and death decisions under strict time and uncertainty constrains. They are afraid of getting a decision wrong, causing unnecessary economic disruption and public anxiety and distress. There is an increasing recognition of the need of combining mathematical models, together with statistical and operations research methods to address disaster management. The interdisciplinary science of mathematics applied to the study of volcanology and volcanic hazard is an important approach which will help understand volcanic processes by integrating keen volcanological insights with sound statistical modeling and artful application of computational power. The aim of this thesis is to work with volcanologists to try and address, with the appropriate statistical methods, those questions they raise, and have volcanologists collaborate with statisticians to learn about the advantages in the application of statistical techniques to the interpretation of volcanic data. Here, we propose and analyze different statistical methodologies to interpret volcanic data and assess volcanic hazard. The statistical technique will depend on the nature of the data and the type of problem we want to address. The models will be used to analyze and interpret the historical and geological volcanic data for Teide-Pico Viejo stratovolcanoes (TPV) and the Canary Islands archipelago. The first statistical method is an Elicitation of Expert Judgment using the so-called Classical Model to assign probabilities of occurrence to each possible eruptive scenario that can be outlined from the eruption history of the volcano, and our knowledge of other analogous volcanoes. The aim was to assess the long-term volcanic hazard of TPV, following an unrest episode in 2004 which created discrepancies among scientists regarding the nature of the unrest and the level of hazard. The second statistical method is a Bayesian Inference approach to compute the long-term probability for each volcanic scenario. The idea to use this method came after seeing the limitations on the Classical Model. The third method is a Non-parametric one-way unbalanced ANOVA using the Kruskal - Wallis test. This study was suggested following the publication for the first time of the World Collapse Caldera Database (WCCD) by the Group of Volcanology of Barcelona. The fourth statistical methodology NHGPP (Non-homogeneous generalized Pareto-Poisson process) uses extreme value theory to study eruptive time series combining geological and historical records. This methodology is applied to the Canary Islands eruptive time series to study volcanic recurrence.