Bayesian Decision Thresholds for Bushfire Warnings: Calibration and Robustness for Rare‐Event Risk

Current bushfire warning systems communicate the probability of a warning given danger, but residents require the probability of danger given a warning. This misalignment, combined with the extreme rarity of catastrophic fires, often leads to the dangerous ‘wait and see’ behaviour. A necessary preliminary result establishes that the Catastrophic fire danger rating system possesses genuine discriminative skill despite the accuracy paradox: a naïve policy of never issuing warnings achieves higher raw accuracy than the actual system; yet, the Peirce Skill Score () demonstrates strongly positive discrimination that no skill‐free forecasting strategy can replicate. The ratio constitutes a triple identity—Bayes factor, positive diagnostic likelihood ratio, and cost‐loss multiplier—that unifies the Bayesian, medical diagnostic and meteorological forecast verification literature. We then develop a calibrated Bayesian decision‐theoretic framework for property‐level bushfire warnings using Australian historical data. By specifying priors for daily threat probability (), likelihoods for Catastrophic ratings and asymmetric loss functions, we derive a closed‐form optimal evacuation threshold. Under baseline calibration, the posterior probability of threat given a Catastrophic rating rises to only . Crucially, however, under realistic asymmetric losses (where the cost of staying during a threat exceeds the cost of evacuating), the optimal decision threshold is even lower (), so ‘leaving early’ is rational even when the absolute probability of fire impact is extremely low. Sensitivity analysis demonstrates that this conclusion is robust across two orders of magnitude in loss ratios and wide ranges of prior probabilities, with the threat‐to‐destruction ratio identified as the key calibration parameter.