Integrating experts' belief in upper tail inference for modelling of human-induced earthquake magnitudes

Yue, Wanchen and Tawn, Jonathan and Towe, Ross and Varty, Zak (2025) Integrating experts' belief in upper tail inference for modelling of human-induced earthquake magnitudes. Journal of Agricultural, Biological, and Environmental Statistics. (In Press)

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Abstract

Accurate estimation of the upper tail of a distribution is crucial in seismology, where estimating the probability of extreme earthquake magnitudes is vital for risk assessment and mitigation. Traditional statistical methods often overlook expert knowledge, particularly regarding physical upper bounds on earthquake magnitudes. This paper introduces a novel methodology for estimating the upper tail distribution, integrating experts' knowledge on the physical processes through a conservative bound on the worst possible earthquakes. The methodology combines rigorous statistical techniques with expert judgement, creating a hybrid model that complements existing data-driven methods and enhances the reliability of tail estimates. We demonstrate the benefits of incorporating experts' knowledge through the application to data on human-induced earthquakes in the Netherlands. Within this paper, we focus on seismological magnitude modelling, however, the proposed methodology has the potential to be implemented as a generic extreme value approach for multiple problem settings.