Bayesian inference in natural hazard analysis for incomplete and uncertain data

This study presents a method for estimating two area-characteristic natural hazard recurrence parameters. The mean activity rate and the frequency–size power law exponent are estimated using Bayesian inference on combined empirical datasets that consist of prehistoric, historic, and instrumental information. The method provides for incompleteness, uncertainty in the event size determination, uncertainty associated with the parameters in the applied occurrence models, and the validity of event occurrences. This aleatory and epistemic uncertainty is introduced in the models through mixture distributions and weighted likelihood functions. The proposed methodology is demonstrated using a synthetic earthquake dataset and an observed tsunami dataset for Japan. The contribution of the different types of data, prior information, and the uncertainty is quantified. For the synthetic dataset, the introduction of model and event size uncertainties provides estimates quite close to the assumed true values, whereas the tsunami dataset shows that the long series of historic data influences the estimates of the recurrence parameters much more than the recent instrumental data. The conclusion of the study is that the proposed methodology provides a useful and adaptable tool for the probabilistic assessment of various types of natural hazards.