It is 1943, and you sit with the Statistical Research Group in Manhattan, staring at maps of returning bombers peppered with bullet holes — dense on the wings and fuselage, sparse on the engines. The generals want armor added where the holes cluster. That instinct is exactly backwards, and lives ride on your seeing why: you are looking only at the planes that made it home. The engine-hit bombers are not in your data because they are at the bottom of the Channel. Decide where the armor truly belongs and formalize the selection effect that makes the naive answer lethal. Get it wrong and you armor the wrong plates, and more crews don't come back — the missing data is the whole message.
Chose LQG control via the separation principle — wrong. Observability and controllability analysis was the one that fit.
Kalman's 1960 filter estimates hidden state from noisy observations, which sounds tantalizingly close to inferring unseen damage from seen damage — but the resemblance is superficial. The filter presumes you receive measurements from the system of interest with known observation noise; the bombers' problem is that an entire stratum of systems sends no measurements at all, and their absence is caused by the hidden variable. Nothing in state-space estimation handles observation processes that censor by outcome; a Kalman filter fitted to survivor data would smoothly and optimally estimate the wrong thing. His engineering-mathematics rigor and his insistence on observability analysis are mildly relevant — observability is exactly what fails here, and he might articulate that failure crisply. But his toolkit arrives seventeen years late and aimed at trajectories, not truncated populations.
Gelman's applied Bayesian workflow is built for exactly this class of error. His survey-adjustment work — multilevel regression and poststratification, and his analyses of nonresponse bias in polling — is modern selection-effect repair: the sample you have differs systematically from the population you want, so model the inclusion mechanism and adjust. In Stan he would write the generative model in an afternoon: per-section hit rates, per-section lethality, survival as a function of hits, likelihood conditioned on return. His teaching writing has used survivorship examples repeatedly, so the diagnosis is instant. What he gives up against the specialists is originality — he applies a now-standard template rather than inventing the formalization — and his computational workflow is seventy years anachronistic for a 1943 desk, though the underlying conditional-probability argument survives translation to hand calculation.
Battle #16 · 8/9/2026, 5:03:58 PM · this result is deterministic: the same two personas on this problem always resolve the same way.