A precise and efficient exceedance-set algorithm for detecting environmental extremes

Inference for predicted exceedance sets is important for various environmental issues such as detecting environmental anomalies and emergencies with high confidence. A critical part is to construct inner and outer predicted exceedance sets using an algorithm that samples from the predictive distribution. The simple currently used sampling procedure can lead to misleading conclusions for some locations due to relatively large standard errors when proportions are estimated from independent observations. Instead we propose an algorithm that calculates probabilities numerically using the Genz–Bretz algorithm, which is based on quasi-random numbers leading to more accurate inner and outer sets, as illustrated on rainfall data in the state of Paraná, Brazil.