Predicting Volcanic Eruptions: Case Study of Rare Events in Chaotic Systems with Delay

Volcanic eruptions can be disastrous; it is therefore important to be able to predict them as accurately as possible. Theoretically, we can use the general machine learning techniques for such predictions. However, in general, without any prior information, such methods require an unrealistic amount of computation time. It is therefore desirable to look for additional information that would enable us to speed up the corresponding computations. In this paper, we provide an empirical evidence that the volcanic system exhibit chaotic and delayed character. We also show that in general (and in volcanic predictions in particular), we can speed up the corresponding predictions if we take into account chaotic and delayed character of the corresponding system.