ModeRisker: Mode-Level Risk Minimization for Scenario Delivery in Probabilistic Forecasting

Consumers of probabilistic forecasts receive $K$ representative scenarios rather than the full predictive distribution, and these scenarios are almost always chosen to optimize average coverage. We show that average-optimal selection undergoes a sharp phase transition: once a mode's probability $\pi$ falls below a threshold set by $K$, the mode is omitted entirely, even though the sample pool still contains it — and rare futures are the reason scenario sets exist. We therefore formalize scenario delivery as mode-level risk minimization: ${\mathrm{CVaR}}_{\beta }$ over per-mode coverage losses. This objective is not submodular, and the natural greedy provably stalls; linearizing at the CVaR supergradient restores near-optimal selection at the same cost. We evaluate with Realized Tail Coverage (${\mathrm{RTC}}_{\beta }$), the CVaR over test instances of the best-of-$K$ distance, under a protocol that stratifies by multimodality and matches $\beta$ to the mode mass, on bifurcation processes and on three real domains with three generator families. Average-greedy delivery collapses from $0.83$ to $0.07$ as $\pi$ drops from $0.02$ to $0.01$ while pool containment stays at $1.0$; ModeRisker tracks the containment bound down to $\pi =2.5/N$ and improves stratified ${\mathrm{RTC}}_{0.01}$ by $39\%$ at no average cost. The bottleneck is mode discovery, not selection: cluster-quality metrics mislead, and an outlier-rescue layer restores near-oracle delivery. Real data delimits the scope: selection pays only where a rare mode is in the pool and the generator is calibrated, and a modality screen keeps the machinery inert elsewhere, which makes the layer safe to deploy by default. Code is available at https://anonymous.4open.science/r/moderisker-CD82.