Estimating rare spatio-temporal precipitation events with conditional extremes

Accurate estimation of rare precipitation events requires methods that capture complex spatial and temporal extremal dependence, especially when extrapolation is needed. This paper presents our team’s contribution to the EVA (2025) Conference Data Challenge, which involves predicting the expected number of high-threshold excesses on a 5 × × 5 spatial grid over 165 years (1850-2014). The targets consider several types of extreme events, including simultaneous extremes at all locations, excesses at multiple sites on the same date, and consecutive-day excesses across subsets of locations. We approach all three targets using a single model, in which temporal dependence is captured through location-specific marginal models, and spatial dependence is implicitly accounted for via a conditional multivariate extreme value model. This modelling strategy, which earned joint second place overall, is broadly applicable to other problems involving rare events with complex spatio-temporal dependence structures.