It is wartime, and sequential methods are being born under the pressure of not wasting a single observation. Now the setting is a dose-finding trial: patients arrive one at a time, and you must choose each one's dosage using everything the earlier patients taught you — too low wastes the chance to help, too high risks harm. You are balancing two goods that pull apart: the welfare of the patient in front of you against knowledge for the thousands who come after. Design the trial that adapts as results arrive and defend the ethics of every escalation. Get it wrong and you either endanger volunteers chasing information or learn too slowly to help anyone — the sequential structure is what makes the trade-off honest.
Chose Observability and controllability analysis — wrong. The Kalman filter was the one that fit.
Kalman's filter (1960) is a recursive, sequential estimator: as each new measurement arrives it updates a state estimate optimally, which is structurally the same online-updating pattern dose-finding needs for tracking an evolving dose-response belief. His state-space formulation naturally handles noisy, sequentially-arriving observations and pairs with control theory for choosing inputs, so a Kalman-plus-control view of dosing is coherent. The mismatch is that his framework assumes linear-Gaussian dynamics and continuous engineering signals, whereas dose-response is nonlinear, binary-outcome (toxicity yes/no), and small-sample. He also brings no notion of patient ethics or the welfare-versus-knowledge trade-off. Kalman gives an elegant recursive-estimation engine and a control-theoretic instinct for closing the loop, but it needs substantial adaptation to the noisy, ethically-bounded, discrete-outcome reality of a dose trial.
Gelman's hierarchical Bayesian workflow and Stan (2010s) give a principled way to pool information across patients while adapting as each new result arrives, which is a natural backbone for adaptive dose-finding: a Bayesian dose-response model updated sequentially, with posterior uncertainty driving the next escalation. Bayesian adaptive designs (CRM-style continual reassessment) are exactly this idea, and Gelman's tools compute them well. He also thinks carefully about model checking and decision-relevant uncertainty. His limits: he is a modeler and applied Bayesian rather than a decision-theorist of stopping rules or an RL specialist, so the formal optimality of escalation and the ethical stopping calculus are less his native turf than Wald's or Murphy's. The posterior-updating machinery he champions is, however, precisely what continual-reassessment dose trials run on.
Battle #14 · 8/9/2026, 5:02:44 PM · this result is deterministic: the same two personas on this problem always resolve the same way.