Models for Temporal Volcanic Hazard

In estimating hazard from a currently quiescent volcano, the most basic quantity of interest is the likelihood of an eruption in some defined time horizon. Starting with the dichotomy of stationarity (where the average future level of activity is equal to the average level of past activity) or non-stationarity, we outline several classes of stochastic models that can be used to forecast future onsets. Renewal models, including the simple Poisson process and mixtures, are compared with models that incorporate volumes of past eruptions, and models that include a trend in the activity level. The mathematical formulations are supplemented by Matlab programs that fit the models using maximum likelihood. Tests are provided for whether a particular model is consistent with the data, and for identifying the best model from those considered. The philosophy behind assumptions and the limitations of each class of models are discussed, and suggestions for further exploration are given. The models are illustrated on a data set of VEI \u3e 1 eruptions from Mt Ruapehu (New Zealand) since 1860