Testing forecasts of a new Bayesian time-predictable model of eruption occurrence

In this paper we propose a model to forecast eruptions in a real forward perspective. Specifically, the model provides a forecast of the next eruption after the end of the last one, using only the data available up to that time. We focus our attention on volcanoes with open conduit regime and high eruption frequency. We assume a generalization of the classical time predictable model to describe the eruptive behavior of open conduit volcanoes and we use a Bayesian hierarchical model to make probabilistic forecasts. We apply the model to Kilauea volcano eruptive data and Mount Etna volcano flank eruption data. The aims of the proposed model are: (1) to test whether or not the Kilauea and Mount Etna volcanoes follow a time predictable behavior; (2) to discuss the volcanological implications of the time predictable model parameters inferred; (3) to compare the forecast capabilities of this model with other models present in literature. The results obtained using the MCMC sampling algorithm show that both volcanoes follow a time predictable behavior. The numerical values inferred for the parameters of the time predictable model suggest that the amount of the erupted volume could change the dynamics of the magma chamber refilling process during the repose period. The probability gain of this model compared with other models already present in literature is appreciably greater than zero. This means that our model provides better forecast than previous models and it could be used in a probabilistic volcanic hazard assessment scheme.