Volcanic time-trend analysis

The use of nonhomogeneous Poisson processes to model volcanic events is increasingly popular, as they allow the inclusion of waxing or waning time-trends and better estimates of future activity. This model also enables the following hypotheses to be tested using simple computational algorithms: (1) Does the historical record of a single volcano show a significantly increasing (or decreasing) time-trend? (2) Is there a significant time-trend difference between two sets of volcanic recurrence interval data? (3) Does a group of volcanoes (≥ 3) show the same time-trend? The historical data of three volcanoes in New Zealand are analyzed to test each of the above hypotheses. A methodology for group model selection based on the hypothesis testing is presented.