Abstract
Modelling point processes with incomplete records is a challenging problem, especially when the degree of record completeness varies over time. For volcanic eruption records, we expect the degree of missingness to depend on both the time and the size of an eruption. We propose a time-varying intensity function for a marked point process to model the non-stationary variation of the observed point process caused by missing data. We apply this model to global and regional volcanic eruption records and use Bayesian inference to obtain hazard estimates and their uncertainties based on the observed incomplete records, to carry out residual analysis and to provide forecasts.